id sid tid token lemma pos cana-5016 1 1 communications communication NOUN cana-5016 1 2 on on ADP cana-5016 1 3 applied apply VERB cana-5016 1 4 nonlinear nonlinear ADJ cana-5016 1 5 analysis analysis NOUN cana-5016 1 6 issn issn NOUN cana-5016 1 7 : : PUNCT cana-5016 1 8 1074 1074 NUM cana-5016 1 9 - - PUNCT cana-5016 1 10 133x 133x NUM cana-5016 1 11 vol vol NOUN cana-5016 1 12 31 31 NUM cana-5016 1 13 no no NOUN cana-5016 1 14 . . PUNCT cana-5016 2 1 8s 8s PROPN cana-5016 2 2 ( ( PUNCT cana-5016 2 3 2024 2024 NUM cana-5016 2 4 ) ) PUNCT cana-5016 2 5 904 904 NUM cana-5016 2 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 2 7 anisotropic anisotropic NOUN cana-5016 2 8 charged charge VERB cana-5016 2 9 spheres sphere NOUN cana-5016 2 10 in in ADP cana-5016 2 11 higher high ADJ cana-5016 2 12 dimensional dimensional PROPN cana-5016 2 13 rosen rosen PROPN cana-5016 2 14 's 's PART cana-5016 2 15 bimetric bimetric ADJ cana-5016 2 16 relativity relativity NOUN cana-5016 2 17 theory theory NOUN cana-5016 2 18 r. r. PROPN cana-5016 2 19 t. t. PROPN cana-5016 2 20 katre1 katre1 PROPN cana-5016 3 1 * * PROPN cana-5016 3 2 , , PUNCT cana-5016 3 3 r. r. PROPN cana-5016 3 4 k. k. PROPN cana-5016 3 5 agrawal2 agrawal2 PROPN cana-5016 3 6 , , PUNCT cana-5016 4 1 s. s. PROPN cana-5016 4 2 d. d. PROPN cana-5016 4 3 tade3 tade3 PROPN cana-5016 5 1 1department 1department NUM cana-5016 5 2 of of ADP cana-5016 5 3 mathematics mathematics PROPN cana-5016 5 4 , , PUNCT cana-5016 5 5 bajaj bajaj PROPN cana-5016 5 6 college college PROPN cana-5016 5 7 of of ADP cana-5016 5 8 science science NOUN cana-5016 5 9 , , PUNCT cana-5016 5 10 wardha wardha PROPN cana-5016 5 11 , , PUNCT cana-5016 5 12 india india PROPN cana-5016 5 13 2department 2department PROPN cana-5016 5 14 of of ADP cana-5016 5 15 mathematics mathematics PROPN cana-5016 5 16 , , PUNCT cana-5016 5 17 hislop hislop PROPN cana-5016 5 18 college college PROPN cana-5016 5 19 , , PUNCT cana-5016 5 20 nagpur nagpur PROPN cana-5016 5 21 , , PUNCT cana-5016 5 22 india india PROPN cana-5016 5 23 3ex 3ex PROPN cana-5016 5 24 - - PUNCT cana-5016 5 25 department department NOUN cana-5016 5 26 of of ADP cana-5016 5 27 mathematics mathematic NOUN cana-5016 5 28 , , PUNCT cana-5016 5 29 jawaharlal jawaharlal PROPN cana-5016 5 30 nehru nehru PROPN cana-5016 5 31 college college PROPN cana-5016 5 32 , , PUNCT cana-5016 5 33 wadi wadi PROPN cana-5016 5 34 , , PUNCT cana-5016 5 35 nagpur nagpur PROPN cana-5016 5 36 ( ( PUNCT cana-5016 5 37 india india PROPN cana-5016 5 38 ) ) PUNCT cana-5016 5 39 * * PUNCT cana-5016 6 1 e e X cana-5016 6 2 - - NOUN cana-5016 6 3 mail mail NOUN cana-5016 6 4 : : PUNCT cana-5016 6 5 katrert9@gmail.com katrert9@gmail.com X cana-5016 6 6 article article NOUN cana-5016 6 7 history history NOUN cana-5016 6 8 : : PUNCT cana-5016 6 9 received receive VERB cana-5016 6 10 : : PUNCT cana-5016 6 11 1 1 NUM cana-5016 6 12 - - SYM cana-5016 6 13 11 11 NUM cana-5016 6 14 - - PUNCT cana-5016 6 15 2024 2024 NUM cana-5016 6 16 revised revise VERB cana-5016 6 17 : : PUNCT cana-5016 6 18 17 17 NUM cana-5016 6 19 - - SYM cana-5016 6 20 12 12 NUM cana-5016 6 21 - - PUNCT cana-5016 6 22 2024 2024 NUM cana-5016 6 23 accepted accept VERB cana-5016 6 24 : : PUNCT cana-5016 6 25 25 25 NUM cana-5016 6 26 - - SYM cana-5016 6 27 12 12 NUM cana-5016 6 28 - - PUNCT cana-5016 6 29 2024 2024 NUM cana-5016 6 30 abstract abstract NOUN cana-5016 6 31 : : PUNCT cana-5016 6 32 in in ADP cana-5016 6 33 the the DET cana-5016 6 34 present present ADJ cana-5016 6 35 study study NOUN cana-5016 6 36 , , PUNCT cana-5016 6 37 we we PRON cana-5016 6 38 presented present VERB cana-5016 6 39 the the DET cana-5016 6 40 field field NOUN cana-5016 6 41 equations equation NOUN cana-5016 6 42 for for ADP cana-5016 6 43 anisotropic anisotropic NOUN cana-5016 6 44 charged charge VERB cana-5016 6 45 spheres sphere NOUN cana-5016 6 46 in in ADP cana-5016 6 47 higher high ADJ cana-5016 6 48 dimensional dimensional ADJ cana-5016 6 49 spherically spherically NOUN cana-5016 6 50 symmetric symmetric ADJ cana-5016 6 51 space space NOUN cana-5016 6 52 - - PUNCT cana-5016 6 53 time time NOUN cana-5016 6 54 in in ADP cana-5016 6 55 the the DET cana-5016 6 56 framework framework NOUN cana-5016 6 57 of of ADP cana-5016 6 58 rosen rosen PROPN cana-5016 6 59 ’s ’s PART cana-5016 6 60 bimetric bimetric ADJ cana-5016 6 61 relativity relativity NOUN cana-5016 6 62 theory theory NOUN cana-5016 6 63 ( ( PUNCT cana-5016 6 64 rosen rosen PROPN cana-5016 6 65 1979 1979 NUM cana-5016 6 66 , , PUNCT cana-5016 6 67 1980 1980 NUM cana-5016 6 68 ) ) PUNCT cana-5016 6 69 . . PUNCT cana-5016 7 1 to to PART cana-5016 7 2 obtain obtain VERB cana-5016 7 3 the the DET cana-5016 7 4 determinate determinate ADJ cana-5016 7 5 solutions solution NOUN cana-5016 7 6 of of ADP cana-5016 7 7 the the DET cana-5016 7 8 higher high ADJ cana-5016 7 9 dimensional dimensional ADJ cana-5016 7 10 field field NOUN cana-5016 7 11 equations equation NOUN cana-5016 7 12 , , PUNCT cana-5016 7 13 the the DET cana-5016 7 14 strategy strategy NOUN cana-5016 7 15 we we PRON cana-5016 7 16 adopted adopt VERB cana-5016 7 17 is be AUX cana-5016 7 18 to to PART cana-5016 7 19 assume assume VERB cana-5016 7 20 that that SCONJ cana-5016 7 21 the the DET cana-5016 7 22 space space NOUN cana-5016 7 23 - - PUNCT cana-5016 7 24 time time NOUN cana-5016 7 25 admits admit VERB cana-5016 7 26 one one NUM cana-5016 7 27 parameter parameter NOUN cana-5016 7 28 group group NOUN cana-5016 7 29 of of ADP cana-5016 7 30 conformal conformal ADJ cana-5016 7 31 motions motion NOUN cana-5016 7 32 generated generate VERB cana-5016 7 33 by by ADP cana-5016 7 34 the the DET cana-5016 7 35 vector vector NOUN cana-5016 7 36 field field NOUN cana-5016 7 37 𝝃𝝁 𝝃𝝁 NOUN cana-5016 7 38 if if SCONJ cana-5016 7 39 lπœ‰π‘”πœ‡πœˆ lπœ‰π‘”πœ‡πœˆ PROPN cana-5016 7 40 = = SYM cana-5016 7 41 πœ“ πœ“ NOUN cana-5016 7 42     SPACE cana-5016 7 43 π‘”πœ‡πœˆ π‘”πœ‡πœˆ NOUN cana-5016 7 44 . . PUNCT cana-5016 8 1 keywords keyword NOUN cana-5016 8 2 : : PUNCT cana-5016 8 3 bimetric bimetric ADJ cana-5016 8 4 theory theory NOUN cana-5016 8 5 , , PUNCT cana-5016 8 6 spherically spherically PROPN cana-5016 8 7 symmetric symmetric PROPN cana-5016 8 8 model model PROPN cana-5016 8 9 1 1 NUM cana-5016 8 10 . . PUNCT cana-5016 9 1 introduction introduction NOUN cana-5016 9 2 rosen rosen PROPN cana-5016 9 3 [ [ X cana-5016 9 4 1 1 NUM cana-5016 9 5 , , PUNCT cana-5016 9 6 2 2 NUM cana-5016 9 7 , , PUNCT cana-5016 9 8 3 3 NUM cana-5016 9 9 ] ] PUNCT cana-5016 9 10 proposed propose VERB cana-5016 9 11 a a DET cana-5016 9 12 new new ADJ cana-5016 9 13 theory theory NOUN cana-5016 9 14 of of ADP cana-5016 9 15 gravitation gravitation NOUN cana-5016 9 16 called call VERB cana-5016 9 17 the the DET cana-5016 9 18 bimetric bimetric ADJ cana-5016 9 19 general general ADJ cana-5016 9 20 relativity relativity NOUN cana-5016 9 21 theory theory NOUN cana-5016 9 22 . . PUNCT cana-5016 10 1 in in ADP cana-5016 10 2 this this DET cana-5016 10 3 theory theory NOUN cana-5016 10 4 , , PUNCT cana-5016 10 5 in in ADP cana-5016 10 6 addition addition NOUN cana-5016 10 7 to to ADP cana-5016 10 8 the the DET cana-5016 10 9 metric metric ADJ cana-5016 10 10 tensor tensor NOUN cana-5016 10 11 𝑔𝑖𝑗 𝑔𝑖𝑗 NOUN cana-5016 10 12 ( ( PUNCT cana-5016 10 13 the the DET cana-5016 10 14 gravitational gravitational ADJ cana-5016 10 15 or or CCONJ cana-5016 10 16 physical physical ADJ cana-5016 10 17 metric metric NOUN cana-5016 10 18 ) ) PUNCT cana-5016 10 19 , , PUNCT cana-5016 10 20 a a DET cana-5016 10 21 second second ADJ cana-5016 10 22 metric metric ADJ cana-5016 10 23 tensor tensor NOUN cana-5016 10 24 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5016 10 25 ( ( PUNCT cana-5016 10 26 the the DET cana-5016 10 27 background background NOUN cana-5016 10 28 metric metric ADJ cana-5016 10 29 ) ) PUNCT cana-5016 10 30 has have AUX cana-5016 10 31 been be AUX cana-5016 10 32 introduced introduce VERB cana-5016 10 33 describing describe VERB cana-5016 10 34 the the DET cana-5016 10 35 geometry geometry NOUN cana-5016 10 36 of of ADP cana-5016 10 37 space space NOUN cana-5016 10 38 - - PUNCT cana-5016 10 39 time time NOUN cana-5016 10 40 , , PUNCT cana-5016 10 41 which which PRON cana-5016 10 42 one one PRON cana-5016 10 43 would would AUX cana-5016 10 44 have have VERB cana-5016 10 45 if if SCONJ cana-5016 10 46 there there PRON cana-5016 10 47 were be VERB cana-5016 10 48 no no DET cana-5016 10 49 matter matter NOUN cana-5016 10 50 in in ADP cana-5016 10 51 the the DET cana-5016 10 52 universe universe NOUN cana-5016 10 53 . . PUNCT cana-5016 11 1 in in ADP cana-5016 11 2 this this DET cana-5016 11 3 respect respect NOUN cana-5016 11 4 the the DET cana-5016 11 5 theory theory NOUN cana-5016 11 6 is be AUX cana-5016 11 7 similar similar ADJ cana-5016 11 8 to to ADP cana-5016 11 9 an an DET cana-5016 11 10 earlier early ADJ cana-5016 11 11 version version NOUN cana-5016 11 12 of of ADP cana-5016 11 13 bimetric bimetric ADJ cana-5016 11 14 theory theory NOUN cana-5016 11 15 formulated formulate VERB cana-5016 11 16 by by ADP cana-5016 11 17 rosen rosen PROPN cana-5016 12 1 [ [ X cana-5016 12 2 4 4 NUM cana-5016 12 3 , , PUNCT cana-5016 12 4 5 5 NUM cana-5016 12 5 , , PUNCT cana-5016 12 6 6 6 NUM cana-5016 12 7 ] ] PUNCT cana-5016 12 8 . . PUNCT cana-5016 13 1 the the DET cana-5016 13 2 field field NOUN cana-5016 13 3 equations equation NOUN cana-5016 13 4 of of ADP cana-5016 13 5 the the DET cana-5016 13 6 present present ADJ cana-5016 13 7 theory theory NOUN cana-5016 13 8 of of ADP cana-5016 13 9 gravitation gravitation NOUN cana-5016 13 10 are be AUX cana-5016 13 11 taken take VERB cana-5016 13 12 to to PART cana-5016 13 13 be be AUX cana-5016 13 14 the the DET cana-5016 13 15 same same ADJ cana-5016 13 16 as as ADP cana-5016 13 17 in in ADP cana-5016 13 18 general general ADJ cana-5016 13 19 relativity relativity NOUN cana-5016 13 20 , , PUNCT cana-5016 13 21 except except SCONJ cana-5016 13 22 for for ADP cana-5016 13 23 the the DET cana-5016 13 24 fact fact NOUN cana-5016 13 25 that that SCONJ cana-5016 13 26 ordinary ordinary ADJ cana-5016 13 27 derivatives derivative NOUN cana-5016 13 28 of of ADP cana-5016 13 29 the the DET cana-5016 13 30 physical physical ADJ cana-5016 13 31 metric metric NOUN cana-5016 13 32 are be AUX cana-5016 13 33 replaced replace VERB cana-5016 13 34 by by ADP cana-5016 13 35 covariant covariant ADJ cana-5016 13 36 derivatives derivative NOUN cana-5016 13 37 with with ADP cana-5016 13 38 respect respect NOUN cana-5016 13 39 to to ADP cana-5016 13 40 the the DET cana-5016 13 41 background background NOUN cana-5016 13 42 metric metric ADJ cana-5016 13 43 . . PUNCT cana-5016 14 1 the the DET cana-5016 14 2 background background NOUN cana-5016 14 3 metric metric ADJ cana-5016 14 4 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5016 14 5 is be AUX cana-5016 14 6 taken take VERB cana-5016 14 7 to to PART cana-5016 14 8 describe describe VERB cana-5016 14 9 a a DET cana-5016 14 10 space space NOUN cana-5016 14 11 - - PUNCT cana-5016 14 12 time time NOUN cana-5016 14 13 of of ADP cana-5016 14 14 constant constant ADJ cana-5016 14 15 curvature curvature NOUN cana-5016 14 16 . . PUNCT cana-5016 15 1 it it PRON cana-5016 15 2 was be AUX cana-5016 15 3 found find VERB cana-5016 15 4 by by ADP cana-5016 15 5 rosen rosen PROPN cana-5016 16 1 [ [ X cana-5016 16 2 2 2 X cana-5016 16 3 ] ] PUNCT cana-5016 16 4 that that SCONJ cana-5016 16 5 these these DET cana-5016 16 6 field field NOUN cana-5016 16 7 equations equation NOUN cana-5016 16 8 could could AUX cana-5016 16 9 be be AUX cana-5016 16 10 written write VERB cana-5016 16 11 in in ADP cana-5016 16 12 the the DET cana-5016 16 13 form form NOUN cana-5016 16 14 of of ADP cana-5016 16 15 einstein einstein ADJ cana-5016 16 16 field field NOUN cana-5016 16 17 equations equation NOUN cana-5016 16 18 , , PUNCT cana-5016 16 19 but but CCONJ cana-5016 16 20 with with ADP cana-5016 16 21 an an DET cana-5016 16 22 additional additional ADJ cana-5016 16 23 term term NOUN cana-5016 16 24 on on ADP cana-5016 16 25 the the DET cana-5016 16 26 right right ADJ cana-5016 16 27 - - PUNCT cana-5016 16 28 hand hand NOUN cana-5016 16 29 side side NOUN cana-5016 16 30 , , PUNCT cana-5016 16 31 𝐺𝑖𝑗 𝐺𝑖𝑗 PROPN cana-5016 16 32 = = PUNCT cana-5016 16 33 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-5016 16 34 βˆ’ βˆ’ PROPN cana-5016 16 35     SPACE cana-5016 17 1 8πœ‹ 8πœ‹ NUM cana-5016 17 2     SPACE cana-5016 17 3 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 17 4 , , PUNCT cana-5016 17 5 ( ( PUNCT cana-5016 17 6 1 1 X cana-5016 17 7 ) ) PUNCT cana-5016 17 8 where where SCONJ cana-5016 17 9 the the DET cana-5016 17 10 einstein einstein PROPN cana-5016 17 11 tensor tensor NOUN cana-5016 17 12 𝐺𝑖𝑗 𝐺𝑖𝑗 PROPN cana-5016 17 13 = = PUNCT cana-5016 17 14 𝑅𝑖𝑗 𝑅𝑖𝑗 PROPN cana-5016 17 15 βˆ’ βˆ’ NOUN cana-5016 17 16 1 1 NUM cana-5016 17 17 2 2 NUM cana-5016 17 18 𝑔𝑖𝑗𝑅 𝑔𝑖𝑗𝑅 NOUN cana-5016 17 19 and and CCONJ cana-5016 17 20 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 17 21 is be AUX cana-5016 17 22 the the DET cana-5016 17 23 energy energy NOUN cana-5016 17 24 - - PUNCT cana-5016 17 25 momentum momentum NOUN cana-5016 17 26 tensor tensor NOUN cana-5016 17 27 of of ADP cana-5016 17 28 the the DET cana-5016 17 29 matter matter NOUN cana-5016 17 30 distribution distribution NOUN cana-5016 17 31 and and CCONJ cana-5016 17 32 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-5016 17 33 = = NOUN cana-5016 17 34 3 3 NUM cana-5016 17 35 π‘Ž2 π‘Ž2 NOUN cana-5016 17 36 ( ( PUNCT cana-5016 17 37 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5016 17 38 βˆ’ βˆ’ PROPN cana-5016 17 39 1 1 NUM cana-5016 17 40 2 2 NUM cana-5016 17 41 π‘”π‘–π‘—π‘”π‘™π‘˜π›Ύπ‘™π‘˜ π‘”π‘–π‘—π‘”π‘™π‘˜π›Ύπ‘™π‘˜ NOUN cana-5016 17 42 ) ) PUNCT cana-5016 17 43 , , PUNCT cana-5016 17 44 ( ( PUNCT cana-5016 17 45 2 2 X cana-5016 17 46 ) ) PUNCT cana-5016 17 47 where where SCONJ cana-5016 17 48 , , PUNCT cana-5016 17 49 π‘Ž π‘Ž NOUN cana-5016 17 50 is be AUX cana-5016 17 51 a a DET cana-5016 17 52 constant constant ADJ cana-5016 17 53 scale scale NOUN cana-5016 17 54 parameter parameter NOUN cana-5016 17 55 , , PUNCT cana-5016 17 56 of of ADP cana-5016 17 57 the the DET cana-5016 17 58 order order NOUN cana-5016 17 59 of of ADP cana-5016 17 60 the the DET cana-5016 17 61 size size NOUN cana-5016 17 62 of of ADP cana-5016 17 63 the the DET cana-5016 17 64 universe universe NOUN cana-5016 17 65 . . PUNCT cana-5016 18 1 mailto:katrert9@gmail.com mailto:katrert9@gmail.com PROPN cana-5016 18 2 communications communication NOUN cana-5016 18 3 on on ADP cana-5016 18 4 applied apply VERB cana-5016 18 5 nonlinear nonlinear ADJ cana-5016 18 6 analysis analysis NOUN cana-5016 18 7 issn issn NOUN cana-5016 18 8 : : PUNCT cana-5016 18 9 1074 1074 NUM cana-5016 18 10 - - PUNCT cana-5016 18 11 133x 133x NUM cana-5016 18 12 vol vol NOUN cana-5016 18 13 31 31 NUM cana-5016 18 14 no no NOUN cana-5016 18 15 . . PUNCT cana-5016 19 1 8s 8s PROPN cana-5016 19 2 ( ( PUNCT cana-5016 19 3 2024 2024 NUM cana-5016 19 4 ) ) PUNCT cana-5016 19 5 905 905 NUM cana-5016 19 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 19 7 from from ADP cana-5016 19 8 this this DET cana-5016 19 9 one one NOUN cana-5016 19 10 sees see VERB cana-5016 19 11 that that SCONJ cana-5016 19 12 , , PUNCT cana-5016 19 13 in in ADP cana-5016 19 14 general general ADJ cana-5016 19 15 , , PUNCT cana-5016 19 16 if if SCONJ cana-5016 19 17 one one PRON cana-5016 19 18 is be AUX cana-5016 19 19 dealing deal VERB cana-5016 19 20 with with ADP cana-5016 19 21 a a DET cana-5016 19 22 physical physical ADJ cana-5016 19 23 system system NOUN cana-5016 19 24 that that PRON cana-5016 19 25 is be AUX cana-5016 19 26 small small ADJ cana-5016 19 27 compared compare VERB cana-5016 19 28 to to ADP cana-5016 19 29 the the DET cana-5016 19 30 size size NOUN cana-5016 19 31 of of ADP cana-5016 19 32 the the DET cana-5016 19 33 universe universe NOUN cana-5016 19 34 , , PUNCT cana-5016 19 35 e.g. e.g. ADV cana-5016 19 36 , , PUNCT cana-5016 19 37 the the DET cana-5016 19 38 solar solar ADJ cana-5016 19 39 system system NOUN cana-5016 19 40 , , PUNCT cana-5016 19 41 then then ADV cana-5016 19 42 the the DET cana-5016 19 43 term term NOUN cana-5016 19 44 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-5016 19 45 is be AUX cana-5016 19 46 negligible negligible ADJ cana-5016 19 47 in in ADP cana-5016 19 48 the the DET cana-5016 19 49 field field NOUN cana-5016 19 50 equations equation NOUN cana-5016 19 51 ( ( PUNCT cana-5016 19 52 1 1 NUM cana-5016 19 53 ) ) PUNCT cana-5016 19 54 and and CCONJ cana-5016 19 55 the the DET cana-5016 19 56 present present ADJ cana-5016 19 57 theory theory NOUN cana-5016 19 58 gives give VERB cana-5016 19 59 agreement agreement NOUN cana-5016 19 60 with with ADP cana-5016 19 61 einstein einstein PROPN cana-5016 19 62 general general ADJ cana-5016 19 63 relativity relativity NOUN cana-5016 19 64 theory theory NOUN cana-5016 19 65 . . PUNCT cana-5016 20 1 in in ADP cana-5016 20 2 recent recent ADJ cana-5016 20 3 years year NOUN cana-5016 20 4 , , PUNCT cana-5016 20 5 the the DET cana-5016 20 6 study study NOUN cana-5016 20 7 of of ADP cana-5016 20 8 higher high ADJ cana-5016 20 9 dimensional dimensional ADJ cana-5016 20 10 space space NOUN cana-5016 20 11 - - PUNCT cana-5016 20 12 time time NOUN cana-5016 20 13 has have AUX cana-5016 20 14 gained gain VERB cana-5016 20 15 momentum momentum NOUN cana-5016 20 16 because because SCONJ cana-5016 20 17 of of ADP cana-5016 20 18 the the DET cana-5016 20 19 fact fact NOUN cana-5016 20 20 that that SCONJ cana-5016 20 21 the the DET cana-5016 20 22 cosmos cosmos PROPN cana-5016 20 23 at at ADP cana-5016 20 24 eats eat NOUN cana-5016 20 25 early early ADJ cana-5016 20 26 stage stage NOUN cana-5016 20 27 of of ADP cana-5016 20 28 evolution evolution NOUN cana-5016 20 29 might might AUX cana-5016 20 30 have have AUX cana-5016 20 31 had have AUX cana-5016 20 32 a a DET cana-5016 20 33 higher high ADJ cana-5016 20 34 dimensional dimensional ADJ cana-5016 20 35 era era NOUN cana-5016 20 36 . . PUNCT cana-5016 21 1 the the DET cana-5016 21 2 extra extra ADJ cana-5016 21 3 space space NOUN cana-5016 21 4 reduced reduce VERB cana-5016 21 5 to to PART cana-5016 21 6 volume volume VERB cana-5016 21 7 with with ADP cana-5016 21 8 passage passage NOUN cana-5016 21 9 of of ADP cana-5016 21 10 time time NOUN cana-5016 21 11 , , PUNCT cana-5016 21 12 which which PRON cana-5016 21 13 is be AUX cana-5016 21 14 beyond beyond ADP cana-5016 21 15 the the DET cana-5016 21 16 ability ability NOUN cana-5016 21 17 of of ADP cana-5016 21 18 experimental experimental ADJ cana-5016 21 19 observations observation NOUN cana-5016 21 20 at at ADP cana-5016 21 21 the the DET cana-5016 21 22 moment moment NOUN cana-5016 21 23 . . PUNCT cana-5016 22 1 also also ADV cana-5016 22 2 , , PUNCT cana-5016 22 3 the the DET cana-5016 22 4 possibility possibility NOUN cana-5016 22 5 that that SCONJ cana-5016 22 6 the the DET cana-5016 22 7 world world NOUN cana-5016 22 8 may may AUX cana-5016 22 9 have have AUX cana-5016 22 10 more more ADJ cana-5016 22 11 than than ADP cana-5016 22 12 4 4 NUM cana-5016 22 13 - - PUNCT cana-5016 22 14 dimensions dimension NOUN cana-5016 22 15 is be AUX cana-5016 22 16 due due ADJ cana-5016 22 17 to to ADP cana-5016 22 18 kaluza kaluza NOUN cana-5016 22 19 [ [ X cana-5016 22 20 7 7 NUM cana-5016 22 21 ] ] PUNCT cana-5016 22 22 and and CCONJ cana-5016 22 23 klein klein PROPN cana-5016 23 1 [ [ X cana-5016 23 2 8 8 NUM cana-5016 23 3 ] ] PUNCT cana-5016 23 4 , , PUNCT cana-5016 23 5 who who PRON cana-5016 23 6 used use VERB cana-5016 23 7 one one NUM cana-5016 23 8 extra extra ADJ cana-5016 23 9 dimension dimension NOUN cana-5016 23 10 to to PART cana-5016 23 11 unify unify VERB cana-5016 23 12 gravity gravity NOUN cana-5016 23 13 and and CCONJ cana-5016 23 14 electromagnetism electromagnetism NOUN cana-5016 23 15 in in ADP cana-5016 23 16 a a DET cana-5016 23 17 theory theory NOUN cana-5016 23 18 that that PRON cana-5016 23 19 was be AUX cana-5016 23 20 essentially essentially ADV cana-5016 23 21 5 5 NUM cana-5016 23 22 - - ADJ cana-5016 23 23 dimensional dimensional ADJ cana-5016 23 24 in in ADP cana-5016 23 25 general general ADJ cana-5016 23 26 relativity relativity NOUN cana-5016 23 27 . . PUNCT cana-5016 24 1 sabbatta sabbatta NOUN cana-5016 24 2 [ [ X cana-5016 24 3 9 9 NUM cana-5016 24 4 ] ] PUNCT cana-5016 24 5 , , PUNCT cana-5016 24 6 lee lee PROPN cana-5016 25 1 [ [ X cana-5016 25 2 10 10 NUM cana-5016 25 3 ] ] PUNCT cana-5016 25 4 , , PUNCT cana-5016 25 5 appelquist appelquist NOUN cana-5016 25 6 and and CCONJ cana-5016 25 7 chodos chodo NOUN cana-5016 26 1 [ [ X cana-5016 26 2 11 11 NUM cana-5016 26 3 ] ] PUNCT cana-5016 26 4 , , PUNCT cana-5016 26 5 and and CCONJ cana-5016 26 6 collins collins PROPN cana-5016 26 7 et et PROPN cana-5016 26 8 al al PROPN cana-5016 26 9 . . PUNCT cana-5016 27 1 [ [ X cana-5016 27 2 12 12 NUM cana-5016 27 3 ] ] PUNCT cana-5016 27 4 accepted accept VERB cana-5016 27 5 this this DET cana-5016 27 6 idea idea NOUN cana-5016 27 7 and and CCONJ cana-5016 27 8 constructed construct VERB cana-5016 27 9 cosmological cosmological ADJ cana-5016 27 10 models model NOUN cana-5016 27 11 in in ADP cana-5016 27 12 higher high ADJ cana-5016 27 13 dimensions dimension NOUN cana-5016 27 14 by by ADP cana-5016 27 15 using use VERB cana-5016 27 16 various various ADJ cana-5016 27 17 phenomena phenomenon NOUN cana-5016 27 18 of of ADP cana-5016 27 19 particle particle NOUN cana-5016 27 20 physics physics NOUN cana-5016 27 21 and and CCONJ cana-5016 27 22 cosmology cosmology PROPN cana-5016 27 23 . . PUNCT cana-5016 28 1 overduin overduin PROPN cana-5016 28 2 and and CCONJ cana-5016 28 3 wesson wesson NOUN cana-5016 29 1 [ [ X cana-5016 29 2 13 13 NUM cana-5016 29 3 ] ] PUNCT cana-5016 29 4 presented present VERB cana-5016 29 5 an an DET cana-5016 29 6 excellent excellent ADJ cana-5016 29 7 review review NOUN cana-5016 29 8 of of ADP cana-5016 29 9 kaluza kaluza PROPN cana-5016 29 10 klein klein PROPN cana-5016 29 11 theory theory PROPN cana-5016 29 12 and and CCONJ cana-5016 29 13 higher higher ADV cana-5016 29 14 - - PUNCT cana-5016 29 15 dimensional dimensional ADJ cana-5016 29 16 unified unified ADJ cana-5016 29 17 theories theory NOUN cana-5016 29 18 , , PUNCT cana-5016 29 19 in in ADP cana-5016 29 20 which which PRON cana-5016 29 21 the the DET cana-5016 29 22 cosmological cosmological ADJ cana-5016 29 23 and and CCONJ cana-5016 29 24 astrophysical astrophysical ADJ cana-5016 29 25 implications implication NOUN cana-5016 29 26 of of ADP cana-5016 29 27 extra extra ADJ cana-5016 29 28 dimensions dimension NOUN cana-5016 29 29 were be AUX cana-5016 29 30 studied study VERB cana-5016 29 31 . . PUNCT cana-5016 30 1 mohanty mohanty NOUN cana-5016 30 2 and and CCONJ cana-5016 30 3 mahanta mahanta ADJ cana-5016 30 4 [ [ X cana-5016 30 5 14 14 NUM cana-5016 30 6 , , PUNCT cana-5016 30 7 15 15 NUM cana-5016 30 8 ] ] PUNCT cana-5016 30 9 , , PUNCT cana-5016 30 10 mohanty mohanty PROPN cana-5016 30 11 and and CCONJ cana-5016 30 12 samanta samanta PROPN cana-5016 31 1 [ [ X cana-5016 31 2 16 16 NUM cana-5016 31 3 ] ] PUNCT cana-5016 31 4 are be AUX cana-5016 31 5 some some PRON cana-5016 31 6 of of ADP cana-5016 31 7 the the DET cana-5016 31 8 authors author NOUN cana-5016 31 9 who who PRON cana-5016 31 10 have have AUX cana-5016 31 11 studied study VERB cana-5016 31 12 higher high ADJ cana-5016 31 13 - - PUNCT cana-5016 31 14 dimensional dimensional ADJ cana-5016 31 15 cosmology cosmology NOUN cana-5016 31 16 in in ADP cana-5016 31 17 various various ADJ cana-5016 31 18 theories theory NOUN cana-5016 31 19 of of ADP cana-5016 31 20 gravitation gravitation NOUN cana-5016 31 21 . . PUNCT cana-5016 32 1 there there PRON cana-5016 32 2 is be VERB cana-5016 32 3 now now ADV cana-5016 32 4 extensive extensive ADJ cana-5016 32 5 literature literature NOUN cana-5016 32 6 dealing deal VERB cana-5016 32 7 with with ADP cana-5016 32 8 different different ADJ cana-5016 32 9 aspects aspect NOUN cana-5016 32 10 of of ADP cana-5016 32 11 higher high ADJ cana-5016 32 12 - - PUNCT cana-5016 32 13 dimensional dimensional ADJ cana-5016 32 14 cosmology cosmology NOUN cana-5016 32 15 . . PUNCT cana-5016 33 1 particularly particularly ADV cana-5016 33 2 , , PUNCT cana-5016 33 3 karade karade NOUN cana-5016 33 4 and and CCONJ cana-5016 33 5 khadekar khadekar NOUN cana-5016 34 1 [ [ X cana-5016 34 2 17 17 NUM cana-5016 34 3 ] ] PUNCT cana-5016 34 4 have have AUX cana-5016 34 5 shown show VERB cana-5016 34 6 non non ADJ cana-5016 34 7 - - NOUN cana-5016 34 8 existence existence NOUN cana-5016 34 9 of of ADP cana-5016 34 10 higher high ADJ cana-5016 34 11 dimensional dimensional ADJ cana-5016 34 12 axially axially ADV cana-5016 34 13 symmetric symmetric ADJ cana-5016 34 14 field field NOUN cana-5016 34 15 in in ADP cana-5016 34 16 rosen rosen PROPN cana-5016 34 17 's 's PART cana-5016 34 18 theory theory NOUN cana-5016 34 19 of of ADP cana-5016 34 20 gravitation gravitation NOUN cana-5016 34 21 . . PUNCT cana-5016 35 1 reddy reddy PROPN cana-5016 35 2 and and CCONJ cana-5016 35 3 venkateswara venkateswara PROPN cana-5016 36 1 [ [ X cana-5016 36 2 18 18 NUM cana-5016 36 3 ] ] PUNCT cana-5016 36 4 have have AUX cana-5016 36 5 shown show VERB cana-5016 36 6 nonexistence nonexistence NOUN cana-5016 36 7 of of ADP cana-5016 36 8 higher high ADJ cana-5016 36 9 dimensional dimensional ADJ cana-5016 36 10 anisotropic anisotropic NOUN cana-5016 36 11 cosmological cosmological ADJ cana-5016 36 12 model model NOUN cana-5016 36 13 in in ADP cana-5016 36 14 bimetric bimetric ADJ cana-5016 36 15 theory theory NOUN cana-5016 36 16 of of ADP cana-5016 36 17 gravitation gravitation NOUN cana-5016 36 18 . . PUNCT cana-5016 37 1 katore katore VERB cana-5016 37 2 et et PROPN cana-5016 37 3 al al PROPN cana-5016 37 4 . . PUNCT cana-5016 38 1 [ [ X cana-5016 38 2 19 19 NUM cana-5016 38 3 ] ] PUNCT cana-5016 38 4 have have AUX cana-5016 38 5 shown show VERB cana-5016 38 6 the the DET cana-5016 38 7 non non ADJ cana-5016 38 8 - - NOUN cana-5016 38 9 existence existence NOUN cana-5016 38 10 of of ADP cana-5016 38 11 n n CCONJ cana-5016 38 12 - - PUNCT cana-5016 38 13 dimensional dimensional ADJ cana-5016 38 14 static static ADJ cana-5016 38 15 plane plane NOUN cana-5016 38 16 symmetric symmetric ADJ cana-5016 38 17 solutions solution NOUN cana-5016 38 18 in in ADP cana-5016 38 19 bimetric bimetric ADJ cana-5016 38 20 relativity relativity NOUN cana-5016 38 21 theory theory NOUN cana-5016 38 22 . . PUNCT cana-5016 39 1 khadekar khadekar PROPN cana-5016 39 2 and and CCONJ cana-5016 39 3 tade tade NOUN cana-5016 39 4 [ [ X cana-5016 39 5 20 20 NUM cana-5016 39 6 ] ] PUNCT cana-5016 39 7 studied study VERB cana-5016 39 8 string string NOUN cana-5016 39 9 cosmological cosmological ADJ cana-5016 39 10 models model NOUN cana-5016 39 11 in in ADP cana-5016 39 12 five five NUM cana-5016 39 13 dimensional dimensional ADJ cana-5016 39 14 bimetric bimetric ADJ cana-5016 39 15 theory theory NOUN cana-5016 39 16 of of ADP cana-5016 39 17 gravitation gravitation NOUN cana-5016 39 18 . . PUNCT cana-5016 40 1 herrera herrera NOUN cana-5016 40 2 et et PROPN cana-5016 40 3 al al PROPN cana-5016 40 4 . . PUNCT cana-5016 41 1 [ [ X cana-5016 41 2 21 21 NUM cana-5016 41 3 ] ] PUNCT cana-5016 41 4 studied study VERB cana-5016 41 5 the the DET cana-5016 41 6 consequences consequence NOUN cana-5016 41 7 of of ADP cana-5016 41 8 inclusion inclusion NOUN cana-5016 41 9 of of ADP cana-5016 41 10 one one NUM cana-5016 41 11 parameter parameter NOUN cana-5016 41 12 group group NOUN cana-5016 41 13 of of ADP cana-5016 41 14 conformal conformal ADJ cana-5016 41 15 motion motion NOUN cana-5016 41 16 of of ADP cana-5016 41 17 anisotropic anisotropic NOUN cana-5016 41 18 matter matter NOUN cana-5016 41 19 in in ADP cana-5016 41 20 the the DET cana-5016 41 21 einstein einstein NOUN cana-5016 41 22 ’s ’s PART cana-5016 41 23 general general ADJ cana-5016 41 24 relativity relativity NOUN cana-5016 41 25 and and CCONJ cana-5016 41 26 obtained obtain VERB cana-5016 41 27 analytical analytical ADJ cana-5016 41 28 solutions solution NOUN cana-5016 41 29 of of ADP cana-5016 41 30 field field NOUN cana-5016 41 31 equations equation NOUN cana-5016 41 32 for for ADP cana-5016 41 33 static static ADJ cana-5016 41 34 and and CCONJ cana-5016 41 35 spherically spherically NOUN cana-5016 41 36 symmetric symmetric ADJ cana-5016 41 37 distribution distribution NOUN cana-5016 41 38 of of ADP cana-5016 41 39 isotropic isotropic NOUN cana-5016 41 40 and and CCONJ cana-5016 41 41 anisotropic anisotropic NOUN cana-5016 41 42 matter matter NOUN cana-5016 41 43 . . PUNCT cana-5016 42 1 the the DET cana-5016 42 2 study study NOUN cana-5016 42 3 of of ADP cana-5016 42 4 static static ADJ cana-5016 42 5 anisotropic anisotropic NOUN cana-5016 42 6 spheres sphere NOUN cana-5016 42 7 is be AUX cana-5016 42 8 important important ADJ cana-5016 42 9 in in ADP cana-5016 42 10 relativistic relativistic ADJ cana-5016 42 11 astrophysics astrophysic NOUN cana-5016 42 12 [ [ X cana-5016 42 13 22 22 NUM cana-5016 42 14 ] ] PUNCT cana-5016 42 15 . . PUNCT cana-5016 43 1 sah sah PROPN cana-5016 43 2 and and CCONJ cana-5016 43 3 prakash prakash PROPN cana-5016 43 4 chandra chandra PROPN cana-5016 44 1 [ [ X cana-5016 44 2 23 23 NUM cana-5016 44 3 ] ] PUNCT cana-5016 44 4 have have AUX cana-5016 44 5 studied study VERB cana-5016 44 6 class class NOUN cana-5016 44 7 of of ADP cana-5016 44 8 charged charge VERB cana-5016 44 9 fluid fluid NOUN cana-5016 44 10 balls ball NOUN cana-5016 44 11 in in ADP cana-5016 44 12 general general ADJ cana-5016 44 13 relativity relativity NOUN cana-5016 44 14 . . PUNCT cana-5016 45 1 hasmani hasmani PROPN cana-5016 45 2 and and CCONJ cana-5016 45 3 pandya pandya PROPN cana-5016 46 1 [ [ X cana-5016 46 2 24 24 NUM cana-5016 46 3 ] ] PUNCT cana-5016 46 4 have have AUX cana-5016 46 5 investigated investigate VERB cana-5016 46 6 cosmological cosmological ADJ cana-5016 46 7 models model NOUN cana-5016 46 8 for for ADP cana-5016 46 9 the the DET cana-5016 46 10 static static ADJ cana-5016 46 11 spherically spherically PROPN cana-5016 46 12 symmetric symmetric ADJ cana-5016 46 13 spacetime spacetime NOUN cana-5016 46 14 with with ADP cana-5016 46 15 charged charge VERB cana-5016 46 16 anisotropic anisotropic NOUN cana-5016 46 17 fluid fluid NOUN cana-5016 46 18 distribution distribution NOUN cana-5016 46 19 in in ADP cana-5016 46 20 ( ( PUNCT cana-5016 46 21 n+2)-dimensions n+2)-dimension NOUN cana-5016 46 22 in in ADP cana-5016 46 23 context context NOUN cana-5016 46 24 of of ADP cana-5016 46 25 rosen rosen PROPN cana-5016 46 26 's 's PART cana-5016 46 27 bimetric bimetric ADJ cana-5016 46 28 general general ADJ cana-5016 46 29 relativity relativity NOUN cana-5016 46 30 . . PUNCT cana-5016 47 1 mukesh mukesh PROPN cana-5016 47 2 kumar kumar PROPN cana-5016 47 3 madhukar madhukar PROPN cana-5016 47 4 [ [ X cana-5016 47 5 25 25 NUM cana-5016 47 6 ] ] PUNCT cana-5016 47 7 presented present VERB cana-5016 47 8 the the DET cana-5016 47 9 study study NOUN cana-5016 47 10 of of ADP cana-5016 47 11 some some DET cana-5016 47 12 charged charge VERB cana-5016 47 13 fluid fluid NOUN cana-5016 47 14 spheres sphere NOUN cana-5016 47 15 in in ADP cana-5016 47 16 general general ADJ cana-5016 47 17 relativity relativity NOUN cana-5016 47 18 solutions solution NOUN cana-5016 47 19 and and CCONJ cana-5016 47 20 conditions condition NOUN cana-5016 47 21 for for ADP cana-5016 47 22 charged charge VERB cana-5016 47 23 fluid fluid NOUN cana-5016 47 24 spheres sphere NOUN cana-5016 47 25 in in ADP cana-5016 47 26 general general ADJ cana-5016 47 27 relativity relativity NOUN cana-5016 47 28 . . PUNCT cana-5016 48 1 francesco francesco PROPN cana-5016 48 2 bajardi bajardi PROPN cana-5016 48 3 and and CCONJ cana-5016 48 4 et et NOUN cana-5016 48 5 . . PUNCT cana-5016 49 1 al al PROPN cana-5016 49 2 . . PUNCT cana-5016 50 1 [ [ X cana-5016 50 2 26 26 NUM cana-5016 50 3 ] ] PUNCT cana-5016 50 4 studied study VERB cana-5016 50 5 the the DET cana-5016 50 6 higher high ADJ cana-5016 50 7 dimensional dimensional ADJ cana-5016 50 8 static static NOUN cana-5016 50 9 and and CCONJ cana-5016 50 10 spherically spherically NOUN cana-5016 50 11 symmetric symmetric ADJ cana-5016 50 12 solutions solution NOUN cana-5016 50 13 in in ADP cana-5016 50 14 extended extended ADJ cana-5016 50 15 gauss gauss ADJ cana-5016 50 16 – – PUNCT cana-5016 50 17 bonnet bonnet NOUN cana-5016 50 18 gravity gravity NOUN cana-5016 50 19 . . PUNCT cana-5016 51 1 recently recently ADV cana-5016 51 2 , , PUNCT cana-5016 51 3 zahraa zahraa PROPN cana-5016 51 4 and and CCONJ cana-5016 51 5 mardanb mardanb NOUN cana-5016 51 6 [ [ X cana-5016 51 7 27 27 NUM cana-5016 51 8 ] ] PUNCT cana-5016 51 9 have have AUX cana-5016 51 10 presented present VERB cana-5016 51 11 five five NUM cana-5016 51 12 - - PUNCT cana-5016 51 13 dimensional dimensional ADJ cana-5016 51 14 analysis analysis NOUN cana-5016 51 15 of of ADP cana-5016 51 16 electromagnetism electromagnetism NOUN cana-5016 51 17 with with ADP cana-5016 51 18 heat heat NOUN cana-5016 51 19 flow flow NOUN cana-5016 51 20 in in ADP cana-5016 51 21 the the DET cana-5016 51 22 post post ADJ cana-5016 51 23 - - ADJ cana-5016 51 24 quasi quasi ADJ cana-5016 51 25 - - ADJ cana-5016 51 26 static static ADJ cana-5016 51 27 approximation approximation NOUN cana-5016 51 28 . . PUNCT cana-5016 52 1 with with ADP cana-5016 52 2 the the DET cana-5016 52 3 above above ADJ cana-5016 52 4 motivation motivation NOUN cana-5016 52 5 , , PUNCT cana-5016 52 6 in in ADP cana-5016 52 7 this this DET cana-5016 52 8 paper paper NOUN cana-5016 52 9 , , PUNCT cana-5016 52 10 we we PRON cana-5016 52 11 have have AUX cana-5016 52 12 presented present VERB cana-5016 52 13 the the DET cana-5016 52 14 field field NOUN cana-5016 52 15 equations equation NOUN cana-5016 52 16 in in ADP cana-5016 52 17 higher high ADJ cana-5016 52 18 dimensional dimensional ADJ cana-5016 52 19 static static ADJ cana-5016 52 20 spherically spherically NOUN cana-5016 52 21 symmetric symmetric ADJ cana-5016 52 22 space space NOUN cana-5016 52 23 - - PUNCT cana-5016 52 24 time time NOUN cana-5016 52 25 in in ADP cana-5016 52 26 the the DET cana-5016 52 27 framework framework NOUN cana-5016 52 28 of of ADP cana-5016 52 29 bimetric bimetric ADJ cana-5016 52 30 theory theory NOUN cana-5016 52 31 of of ADP cana-5016 52 32 relativity relativity NOUN cana-5016 52 33 proposed propose VERB cana-5016 52 34 by by ADP cana-5016 52 35 rosen rosen PROPN cana-5016 53 1 [ [ X cana-5016 53 2 2 2 NUM cana-5016 53 3 , , PUNCT cana-5016 53 4 3 3 NUM cana-5016 53 5 ] ] PUNCT cana-5016 53 6 for for ADP cana-5016 53 7 anisotropic anisotropic NOUN cana-5016 53 8 distribution distribution NOUN cana-5016 53 9 of of ADP cana-5016 53 10 matter matter NOUN cana-5016 53 11 and and CCONJ cana-5016 53 12 also also ADV cana-5016 53 13 obtain obtain VERB cana-5016 53 14 the the DET cana-5016 53 15 solutions solution NOUN cana-5016 53 16 for for ADP cana-5016 53 17 the the DET cana-5016 53 18 physical physical ADJ cana-5016 53 19 metric metric NOUN cana-5016 53 20 with with ADP cana-5016 53 21 the the DET cana-5016 53 22 assumption assumption NOUN cana-5016 53 23 that that SCONJ cana-5016 53 24 the the DET cana-5016 53 25 space space NOUN cana-5016 53 26 - - PUNCT cana-5016 53 27 time time NOUN cana-5016 53 28 admits admit VERB cana-5016 53 29 a a DET cana-5016 53 30 one one NUM cana-5016 53 31 - - PUNCT cana-5016 53 32 parameter parameter NOUN cana-5016 53 33 group group NOUN cana-5016 53 34 of of ADP cana-5016 53 35 conformal conformal ADJ cana-5016 53 36 motions motion NOUN cana-5016 53 37 . . PUNCT cana-5016 54 1 this this DET cana-5016 54 2 work work NOUN cana-5016 54 3 is be AUX cana-5016 54 4 a a DET cana-5016 54 5 generalization generalization NOUN cana-5016 54 6 of of ADP cana-5016 54 7 the the DET cana-5016 54 8 results result NOUN cana-5016 54 9 of of ADP cana-5016 54 10 hererra hererra NOUN cana-5016 54 11 et et PROPN cana-5016 54 12 al al PROPN cana-5016 54 13 . . PUNCT cana-5016 55 1 [ [ X cana-5016 55 2 21 21 NUM cana-5016 55 3 ] ] PUNCT cana-5016 55 4 obtained obtain VERB cana-5016 55 5 in in ADP cana-5016 55 6 general general ADJ cana-5016 55 7 relativity relativity NOUN cana-5016 55 8 to to ADP cana-5016 55 9 the the DET cana-5016 55 10 communications communication NOUN cana-5016 55 11 on on ADP cana-5016 55 12 applied apply VERB cana-5016 55 13 nonlinear nonlinear ADJ cana-5016 55 14 analysis analysis NOUN cana-5016 55 15 issn issn NOUN cana-5016 55 16 : : PUNCT cana-5016 55 17 1074 1074 NUM cana-5016 55 18 - - PUNCT cana-5016 55 19 133x 133x NUM cana-5016 55 20 vol vol NOUN cana-5016 55 21 31 31 NUM cana-5016 55 22 no no NOUN cana-5016 55 23 . . PUNCT cana-5016 56 1 8s 8s PROPN cana-5016 56 2 ( ( PUNCT cana-5016 56 3 2024 2024 NUM cana-5016 56 4 ) ) PUNCT cana-5016 56 5 906 906 NUM cana-5016 56 6 https://internationalpubls.com https://internationalpubls.com NUM cana-5016 56 7 higher high ADJ cana-5016 56 8 dimensional dimensional ADJ cana-5016 56 9 bimetric bimetric ADJ cana-5016 56 10 theory theory NOUN cana-5016 56 11 of of ADP cana-5016 56 12 relativity relativity NOUN cana-5016 56 13 proposed propose VERB cana-5016 56 14 by by ADP cana-5016 56 15 rosen rosen PROPN cana-5016 56 16 . . PUNCT cana-5016 57 1 the the DET cana-5016 57 2 solution solution NOUN cana-5016 57 3 gives give VERB cana-5016 57 4 agreement agreement NOUN cana-5016 57 5 with with ADP cana-5016 57 6 einstein einstein PROPN cana-5016 57 7 ’s ’s PART cana-5016 57 8 general general ADJ cana-5016 57 9 relativity relativity NOUN cana-5016 57 10 for for ADP cana-5016 57 11 physical physical ADJ cana-5016 57 12 system system NOUN cana-5016 57 13 known know VERB cana-5016 57 14 in in ADP cana-5016 57 15 the the DET cana-5016 57 16 universe universe NOUN cana-5016 57 17 , , PUNCT cana-5016 57 18 such such ADJ cana-5016 57 19 as as ADP cana-5016 57 20 the the DET cana-5016 57 21 solar solar ADJ cana-5016 57 22 system system NOUN cana-5016 57 23 . . PUNCT cana-5016 58 1 the the DET cana-5016 58 2 work work NOUN cana-5016 58 3 done do VERB cana-5016 58 4 , , PUNCT cana-5016 58 5 in in ADP cana-5016 58 6 this this DET cana-5016 58 7 paper paper NOUN cana-5016 58 8 , , PUNCT cana-5016 58 9 is be AUX cana-5016 58 10 organized organize VERB cana-5016 58 11 as as SCONJ cana-5016 58 12 follows follow VERB cana-5016 58 13 : : PUNCT cana-5016 58 14 in in ADP cana-5016 58 15 section-2 section-2 NUM cana-5016 58 16 , , PUNCT cana-5016 58 17 we we PRON cana-5016 58 18 obtain obtain VERB cana-5016 58 19 the the DET cana-5016 58 20 field field NOUN cana-5016 58 21 equations equation NOUN cana-5016 58 22 in in ADP cana-5016 58 23 the the DET cana-5016 58 24 presence presence NOUN cana-5016 58 25 of of ADP cana-5016 58 26 an an DET cana-5016 58 27 anisotropic anisotropic NOUN cana-5016 58 28 charged charge VERB cana-5016 58 29 spherically spherically NOUN cana-5016 58 30 symmetric symmetric ADJ cana-5016 58 31 matter matter NOUN cana-5016 58 32 in in ADP cana-5016 58 33 the the DET cana-5016 58 34 frame frame NOUN cana-5016 58 35 work work NOUN cana-5016 58 36 of of ADP cana-5016 58 37 higher high ADJ cana-5016 58 38 dimensional dimensional ADJ cana-5016 58 39 bimetric bimetric ADJ cana-5016 58 40 theory theory NOUN cana-5016 58 41 of of ADP cana-5016 58 42 relativity relativity NOUN cana-5016 58 43 proposed propose VERB cana-5016 58 44 by by ADP cana-5016 58 45 rosen rosen PROPN cana-5016 59 1 [ [ X cana-5016 59 2 2 2 NUM cana-5016 59 3 , , PUNCT cana-5016 59 4 3 3 NUM cana-5016 59 5 ] ] PUNCT cana-5016 59 6 . . PUNCT cana-5016 60 1 section-3 section-3 NUM cana-5016 60 2 deals deal NOUN cana-5016 60 3 with with ADP cana-5016 60 4 the the DET cana-5016 60 5 solutions solution NOUN cana-5016 60 6 of of ADP cana-5016 60 7 the the DET cana-5016 60 8 field field NOUN cana-5016 60 9 equations equation NOUN cana-5016 60 10 under under ADP cana-5016 60 11 the the DET cana-5016 60 12 assumption assumption NOUN cana-5016 60 13 that that SCONJ cana-5016 60 14 the the DET cana-5016 60 15 space space NOUN cana-5016 60 16 time time NOUN cana-5016 60 17 admits admit VERB cana-5016 60 18 a a DET cana-5016 60 19 one one NUM cana-5016 60 20 - - PUNCT cana-5016 60 21 parameter parameter NOUN cana-5016 60 22 group group NOUN cana-5016 60 23 of of ADP cana-5016 60 24 conformal conformal ADJ cana-5016 60 25 motions motion NOUN cana-5016 60 26 [ [ X cana-5016 60 27 herrera herrera NOUN cana-5016 60 28 et et PROPN cana-5016 60 29 al al PROPN cana-5016 60 30 . . PROPN cana-5016 61 1 ( ( PUNCT cana-5016 61 2 1985 1985 NUM cana-5016 61 3 ) ) PUNCT cana-5016 61 4 ] ] PUNCT cana-5016 62 1 generated generate VERB cana-5016 62 2 by by ADP cana-5016 62 3 the the DET cana-5016 62 4 vector vector NOUN cana-5016 62 5 field field NOUN cana-5016 62 6 πœ‰πœ‡ πœ‰πœ‡ NOUN cana-5016 62 7 if if SCONJ cana-5016 62 8 lπœ‰π‘”πœ‡πœˆ lπœ‰π‘”πœ‡πœˆ PROPN cana-5016 62 9 = = SYM cana-5016 62 10 πœ“ πœ“ NOUN cana-5016 62 11     SPACE cana-5016 62 12 π‘”πœ‡πœˆ π‘”πœ‡πœˆ NOUN cana-5016 62 13 , , PUNCT cana-5016 62 14 ( ( PUNCT cana-5016 62 15 1 1 X cana-5016 62 16 ) ) PUNCT cana-5016 62 17 where where SCONJ cana-5016 62 18 l.h.s l.h.s NOUN cana-5016 62 19 . . PUNCT cana-5016 63 1 of of ADP cana-5016 63 2 ( ( PUNCT cana-5016 63 3 1 1 X cana-5016 63 4 ) ) PUNCT cana-5016 63 5 is be AUX cana-5016 63 6 the the DET cana-5016 63 7 lie lie NOUN cana-5016 63 8 derivative derivative ADJ cana-5016 63 9 operator operator NOUN cana-5016 63 10 and and CCONJ cana-5016 63 11 πœ“ πœ“ NOUN cana-5016 63 12 is be AUX cana-5016 63 13 conformal conformal ADJ cana-5016 63 14 factor factor NOUN cana-5016 63 15 . . PUNCT cana-5016 64 1 section-4 section-4 NUM cana-5016 64 2 contains contain VERB cana-5016 64 3 some some DET cana-5016 64 4 conclusions conclusion NOUN cana-5016 64 5 . . PUNCT cana-5016 65 1 2 2 X cana-5016 65 2 . . X cana-5016 65 3 metric metric ADJ cana-5016 65 4 and and CCONJ cana-5016 65 5 field field NOUN cana-5016 65 6 equations equation NOUN cana-5016 65 7 we we PRON cana-5016 65 8 consider consider VERB cana-5016 65 9 the the DET cana-5016 65 10 higher high ADJ cana-5016 65 11 dimensional dimensional ADJ cana-5016 65 12 static static ADJ cana-5016 65 13 distribution distribution NOUN cana-5016 65 14 of of ADP cana-5016 65 15 matter matter NOUN cana-5016 65 16 represented represent VERB cana-5016 65 17 by by ADP cana-5016 65 18 charged charge VERB cana-5016 65 19 spherically spherically PROPN cana-5016 65 20 symmetric symmetric ADJ cana-5016 65 21 fluid fluid NOUN cana-5016 65 22 which which PRON cana-5016 65 23 may may AUX cana-5016 65 24 be be AUX cana-5016 65 25 anisotropic anisotropic NOUN cana-5016 65 26 . . PUNCT cana-5016 66 1 in in ADP cana-5016 66 2 terms term NOUN cana-5016 66 3 of of ADP cana-5016 66 4 schwarzschild schwarzschild NOUN cana-5016 66 5 coordinates coordinate VERB cana-5016 66 6 the the DET cana-5016 66 7 physical physical ADJ cana-5016 66 8 metric metric NOUN cana-5016 66 9 takes take VERB cana-5016 66 10 the the DET cana-5016 66 11 form form NOUN cana-5016 66 12 𝑑𝑠2 𝑑𝑠2 NOUN cana-5016 66 13 = = NOUN cana-5016 66 14 π‘’πœˆπ‘‘π‘‘2 π‘’πœˆπ‘‘π‘‘2 NOUN cana-5016 67 1 βˆ’ βˆ’ NOUN cana-5016 67 2 π‘’πœ†π‘‘π‘Ÿ2 π‘’πœ†π‘‘π‘Ÿ2 NOUN cana-5016 67 3 βˆ’ βˆ’ ADP cana-5016 67 4 π‘Ÿ2𝑑𝛺2 π‘Ÿ2𝑑𝛺2 NUM cana-5016 67 5 , , PUNCT cana-5016 67 6 ( ( PUNCT cana-5016 67 7 2 2 X cana-5016 67 8 ) ) PUNCT cana-5016 67 9 where where SCONJ cana-5016 67 10 𝑑𝛺2 𝑑𝛺2 PUNCT cana-5016 68 1 = = NOUN cana-5016 68 2 π‘‘πœƒ1 π‘‘πœƒ1 NOUN cana-5016 68 3 2 2 NUM cana-5016 68 4 + + NUM cana-5016 68 5 𝑠𝑖𝑛2 𝑠𝑖𝑛2 NOUN cana-5016 68 6 πœƒ1 πœƒ1 NOUN cana-5016 68 7 π‘‘πœƒ2 π‘‘πœƒ2 NOUN cana-5016 68 8 2 2 NUM cana-5016 69 1 + + NOUN cana-5016 69 2 𝑠𝑖𝑛2 𝑠𝑖𝑛2 NOUN cana-5016 69 3 πœƒ1 πœƒ1 NOUN cana-5016 69 4     SPACE cana-5016 69 5 𝑠𝑖𝑛2 𝑠𝑖𝑛2 NOUN cana-5016 69 6 πœƒ3 πœƒ3 ADJ cana-5016 69 7 π‘‘πœƒ3 π‘‘πœƒ3 NOUN cana-5016 69 8 2 2 NUM cana-5016 69 9 + + CCONJ cana-5016 69 10 β‹― β‹― VERB cana-5016 69 11 + + CCONJ cana-5016 69 12 [ [ PUNCT cana-5016 69 13 ∏ ∏ NUM cana-5016 69 14 𝑖=1 𝑖=1 PUNCT cana-5016 69 15 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-5016 69 16 𝑠𝑖𝑛2 𝑠𝑖𝑛2 NOUN cana-5016 69 17 πœƒπ‘– πœƒπ‘– X cana-5016 69 18 ] ] PUNCT cana-5016 69 19     SPACE cana-5016 69 20 π‘‘πœƒπ‘› π‘‘πœƒπ‘› VERB cana-5016 69 21 2 2 NUM cana-5016 69 22 and and CCONJ cana-5016 69 23 πœ† πœ† NOUN cana-5016 69 24 , , PUNCT cana-5016 69 25 𝜈 𝜈 PROPN cana-5016 69 26 are be AUX cana-5016 69 27 the the DET cana-5016 69 28 functions function NOUN cana-5016 69 29 of of ADP cana-5016 69 30 π‘Ÿ π‘Ÿ NOUN cana-5016 69 31 only only ADV cana-5016 69 32 . . PUNCT cana-5016 70 1 with with ADP cana-5016 70 2 this this DET cana-5016 70 3 choice choice NOUN cana-5016 70 4 of of ADP cana-5016 70 5 coordinates coordinate NOUN cana-5016 70 6 the the DET cana-5016 70 7 total total ADJ cana-5016 70 8 energy energy NOUN cana-5016 70 9 - - PUNCT cana-5016 70 10 momentum momentum NOUN cana-5016 70 11 tensor tensor NOUN cana-5016 70 12 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 70 13 is be AUX cana-5016 70 14 assumed assume VERB cana-5016 70 15 to to PART cana-5016 70 16 be be AUX cana-5016 70 17 the the DET cana-5016 70 18 sum sum NOUN cana-5016 70 19 of of ADP cana-5016 70 20 two two NUM cana-5016 70 21 parts part NOUN cana-5016 70 22 , , PUNCT cana-5016 70 23 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 70 24 𝐴 𝐴 PROPN cana-5016 70 25 and and CCONJ cana-5016 70 26 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 70 27 𝐸 𝐸 PROPN cana-5016 70 28 , , PUNCT cana-5016 70 29 i.e. i.e. X cana-5016 70 30 𝑇𝑖𝑗 𝑇𝑖𝑗 NOUN cana-5016 70 31 = = SYM cana-5016 70 32 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 70 33 𝐴 𝐴 NOUN cana-5016 70 34 + + CCONJ cana-5016 70 35 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 70 36 𝐸 𝐸 PROPN cana-5016 70 37 . . PUNCT cana-5016 71 1 ( ( PUNCT cana-5016 71 2 3 3 X cana-5016 71 3 ) ) PUNCT cana-5016 71 4 here here ADV cana-5016 71 5 π‘»π’Šπ’‹ π‘»π’Šπ’‹ PROPN cana-5016 71 6 𝑨 𝑨 PROPN cana-5016 71 7 is be AUX cana-5016 71 8 an an DET cana-5016 71 9 anisotropic anisotropic NOUN cana-5016 71 10 spherically spherically NOUN cana-5016 71 11 symmetric symmetric ADJ cana-5016 71 12 matter matter NOUN cana-5016 71 13 distribution distribution NOUN cana-5016 71 14 and and CCONJ cana-5016 71 15 is be AUX cana-5016 71 16 given give VERB cana-5016 71 17 by by ADP cana-5016 71 18 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5016 71 19 𝐴 𝐴 NOUN cana-5016 71 20 = = SYM cana-5016 71 21 ( ( PUNCT cana-5016 71 22 πœŒπ‘š πœŒπ‘š X cana-5016 71 23 + + CCONJ cana-5016 71 24 𝑃βŠ₯ 𝑃βŠ₯ NOUN cana-5016 71 25 ) ) PUNCT cana-5016 71 26     SPACE cana-5016 72 1 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 72 2     SPACE cana-5016 72 3 π‘ˆπ‘— π‘ˆπ‘— PROPN cana-5016 72 4 βˆ’ βˆ’ PROPN cana-5016 72 5 𝑃βŠ₯𝑔𝑖𝑗 𝑃βŠ₯𝑔𝑖𝑗 NOUN cana-5016 72 6 + + CCONJ cana-5016 72 7 ( ( PUNCT cana-5016 72 8 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-5016 72 9 βˆ’ βˆ’ PROPN cana-5016 72 10 𝑃βŠ₯ 𝑃βŠ₯ NOUN cana-5016 72 11 ) ) PUNCT cana-5016 72 12     SPACE cana-5016 72 13 πœ’π‘– πœ’π‘– NOUN cana-5016 72 14     SPACE cana-5016 72 15 πœ’π‘— πœ’π‘— VERB cana-5016 72 16 , , PUNCT cana-5016 72 17 ( ( PUNCT cana-5016 72 18 4 4 X cana-5016 72 19 ) ) PUNCT cana-5016 72 20 where where SCONJ cana-5016 72 21 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 72 22 is be AUX cana-5016 72 23 the the DET cana-5016 72 24 time time NOUN cana-5016 72 25 like like ADP cana-5016 72 26 ( ( PUNCT cana-5016 72 27 𝑛 𝑛 PROPN cana-5016 72 28 + + NOUN cana-5016 72 29 2 2 NUM cana-5016 72 30 ) ) PUNCT cana-5016 72 31 -velocity -velocity NOUN cana-5016 72 32 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 72 33 = = PUNCT cana-5016 72 34 𝛿(𝑛+2 𝛿(𝑛+2 PROPN cana-5016 72 35 ) ) PUNCT cana-5016 72 36 𝑖 𝑖 SYM cana-5016 73 1 π‘’βˆ’πœˆ/2 π‘’βˆ’πœˆ/2 PROPN cana-5016 73 2 , , PUNCT cana-5016 73 3 πœ’π‘– πœ’π‘– PROPN cana-5016 73 4 a a DET cana-5016 73 5 unit unit NOUN cana-5016 73 6 space space NOUN cana-5016 73 7 - - PUNCT cana-5016 73 8 like like ADJ cana-5016 73 9 vector vector NOUN cana-5016 73 10 in in ADP cana-5016 73 11 the the DET cana-5016 73 12 radial radial ADJ cana-5016 73 13 direction direction NOUN cana-5016 73 14 πœ’π‘– πœ’π‘– PROPN cana-5016 73 15 = = PUNCT cana-5016 73 16 𝛿1 𝛿1 PROPN cana-5016 73 17 π‘–π‘’βˆ’πœ†/2 π‘–π‘’βˆ’πœ†/2 PROPN cana-5016 73 18 , , PUNCT cana-5016 73 19 πœŒπ‘š πœŒπ‘š VERB cana-5016 73 20 the the DET cana-5016 73 21 energy energy NOUN cana-5016 73 22 density density NOUN cana-5016 73 23 , , PUNCT cana-5016 73 24 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-5016 73 25 the the DET cana-5016 73 26 radial radial ADJ cana-5016 73 27 pressure pressure NOUN cana-5016 73 28 in in ADP cana-5016 73 29 the the DET cana-5016 73 30 direction direction NOUN cana-5016 73 31 of of ADP cana-5016 73 32 πœ’π‘– πœ’π‘– PROPN cana-5016 73 33 and and CCONJ cana-5016 73 34 𝑃βŠ₯ 𝑃βŠ₯ VERB cana-5016 73 35 the the DET cana-5016 73 36 pressure pressure NOUN cana-5016 73 37 orthogonal orthogonal NOUN cana-5016 73 38 to to PART cana-5016 73 39 πœ’π‘–. πœ’π‘–. VERB cana-5016 73 40 similarly similarly ADV cana-5016 73 41 , , PUNCT cana-5016 73 42 the the DET cana-5016 73 43 electromagnetic electromagnetic ADJ cana-5016 73 44 contribution contribution NOUN cana-5016 73 45 can can AUX cana-5016 73 46 be be AUX cana-5016 73 47 written write VERB cana-5016 73 48 as as ADP cana-5016 73 49 π‘»π’Šπ’‹ π‘»π’Šπ’‹ PROPN cana-5016 73 50 𝑬 𝑬 PROPN cana-5016 73 51 = = SYM cana-5016 73 52 βˆ’ βˆ’ NOUN cana-5016 73 53 𝟏 𝟏 NUM cana-5016 73 54 πŸ’π… πŸ’π… NOUN cana-5016 73 55 ( ( PUNCT cana-5016 73 56 π‘­π’Š π‘­π’Š PROPN cana-5016 73 57 πœΆπ‘­π’‹πœΆ πœΆπ‘­π’‹πœΆ PROPN cana-5016 73 58 βˆ’ βˆ’ PROPN cana-5016 73 59 𝟏 𝟏 NUM cana-5016 73 60 πŸ’ πŸ’ PROPN cana-5016 73 61 π’ˆπ’Šπ’‹ π’ˆπ’Šπ’‹ NOUN cana-5016 73 62     SPACE cana-5016 73 63 π‘­π’π’Œπ‘­π’π’Œ π‘­π’π’Œπ‘­π’π’Œ NOUN cana-5016 73 64 ) ) PUNCT cana-5016 73 65 , , PUNCT cana-5016 73 66 ( ( PUNCT cana-5016 73 67 5 5 X cana-5016 73 68 ) ) PUNCT cana-5016 73 69 where where SCONJ cana-5016 73 70 π‘­π’Šπ’‹ π‘­π’Šπ’‹ PROPN cana-5016 73 71 is be AUX cana-5016 73 72 the the DET cana-5016 73 73 electromagnetic electromagnetic ADJ cana-5016 73 74 field field NOUN cana-5016 73 75 tensor tensor NOUN cana-5016 73 76 defined define VERB cana-5016 73 77 in in ADP cana-5016 73 78 terms term NOUN cana-5016 73 79 of of ADP cana-5016 73 80 the the DET cana-5016 73 81 ( ( PUNCT cana-5016 73 82 𝒏 𝒏 PROPN cana-5016 73 83 + + CCONJ cana-5016 73 84 𝟐)-potential 𝟐)-potential PROPN cana-5016 73 85 π‘¨π’Š π‘¨π’Š PROPN cana-5016 73 86 as as ADP cana-5016 73 87 π‘­π’Šπ’‹ π‘­π’Šπ’‹ PROPN cana-5016 73 88 = = SYM cana-5016 73 89 π‘¨π’Š π‘¨π’Š PROPN cana-5016 73 90 , , PUNCT cana-5016 73 91     SPACE cana-5016 73 92 𝒋 𝒋 NOUN cana-5016 73 93 βˆ’ βˆ’ PROPN cana-5016 73 94 𝑨𝒋,π’Š 𝑨𝒋,π’Š PROPN cana-5016 73 95 . . PUNCT cana-5016 74 1 ( ( PUNCT cana-5016 74 2 6 6 X cana-5016 74 3 ) ) PUNCT cana-5016 74 4 communications communication NOUN cana-5016 74 5 on on ADP cana-5016 74 6 applied apply VERB cana-5016 74 7 nonlinear nonlinear ADJ cana-5016 74 8 analysis analysis NOUN cana-5016 74 9 issn issn NOUN cana-5016 74 10 : : PUNCT cana-5016 74 11 1074 1074 NUM cana-5016 74 12 - - PUNCT cana-5016 74 13 133x 133x NUM cana-5016 74 14 vol vol NOUN cana-5016 74 15 31 31 NUM cana-5016 74 16 no no NOUN cana-5016 74 17 . . PUNCT cana-5016 75 1 8s 8s PROPN cana-5016 75 2 ( ( PUNCT cana-5016 75 3 2024 2024 NUM cana-5016 75 4 ) ) PUNCT cana-5016 75 5 907 907 NUM cana-5016 75 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 75 7 as as SCONJ cana-5016 75 8 the the DET cana-5016 75 9 frame frame NOUN cana-5016 75 10 is be AUX cana-5016 75 11 considered consider VERB cana-5016 75 12 to to PART cana-5016 75 13 be be AUX cana-5016 75 14 the the DET cana-5016 75 15 rest rest NOUN cana-5016 75 16 frame frame NOUN cana-5016 75 17 , , PUNCT cana-5016 75 18 we we PRON cana-5016 75 19 adopt adopt VERB cana-5016 75 20 the the DET cana-5016 75 21 gauge gauge NOUN cana-5016 76 1 π‘¨π’Š π‘¨π’Š PROPN cana-5016 76 2 = = SYM cana-5016 76 3 π‘¨π’Š(𝟎 π‘¨π’Š(𝟎 ADJ cana-5016 76 4 , , PUNCT cana-5016 76 5     SPACE cana-5016 76 6 𝟎 𝟎 NUM cana-5016 76 7 , , PUNCT cana-5016 76 8     SPACE cana-5016 76 9 𝟎 𝟎 NUM cana-5016 76 10 , , PUNCT cana-5016 76 11     SPACE cana-5016 76 12 β‹― β‹― PROPN cana-5016 76 13 ( ( PUNCT cana-5016 76 14 𝒏 𝒏 PROPN cana-5016 76 15 + + NOUN cana-5016 76 16 𝟏 𝟏 X cana-5016 76 17 ) ) PUNCT cana-5016 76 18     SPACE cana-5016 76 19 π’•π’Šπ’Žπ’†π’” π’•π’Šπ’Žπ’†π’” NOUN cana-5016 76 20     SPACE cana-5016 76 21 , , PUNCT cana-5016 76 22 𝝋(𝒓 𝝋(𝒓 PROPN cana-5016 76 23 ) ) PUNCT cana-5016 76 24 ) ) PUNCT cana-5016 76 25 . . PUNCT cana-5016 77 1 also also ADV cana-5016 77 2 , , PUNCT cana-5016 77 3 π‘­π’Šπ’‹ π‘­π’Šπ’‹ PROPN cana-5016 77 4 satisfy satisfy VERB cana-5016 77 5 the the DET cana-5016 77 6 einstein einstein PROPN cana-5016 77 7 - - PUNCT cana-5016 77 8 maxwell maxwell PROPN cana-5016 77 9 field field NOUN cana-5016 77 10 equations equation NOUN cana-5016 77 11 𝐹𝑖𝑗;π‘˜ 𝐹𝑖𝑗;π‘˜ PUNCT cana-5016 78 1 + + SYM cana-5016 78 2 πΉπ‘—π‘˜;𝑖 πΉπ‘—π‘˜;𝑖 NUM cana-5016 78 3 + + CCONJ cana-5016 78 4 πΉπ‘˜π‘–;𝑗 πΉπ‘˜π‘–;𝑗 PUNCT cana-5016 78 5 = = SYM cana-5016 78 6 0 0 NUM cana-5016 78 7 , , PUNCT cana-5016 78 8 ( ( PUNCT cana-5016 78 9 7 7 X cana-5016 78 10 ) ) PUNCT cana-5016 78 11 𝐹;𝑗 𝐹;𝑗 NOUN cana-5016 78 12 𝑖𝑗 𝑖𝑗 X cana-5016 78 13 = = PUNCT cana-5016 78 14 βˆ’4πœ‹ βˆ’4πœ‹ NOUN cana-5016 78 15     SPACE cana-5016 78 16 𝐽𝑖 𝐽𝑖 PROPN cana-5016 78 17 , , PUNCT cana-5016 78 18 ( ( PUNCT cana-5016 78 19 8) 8) NUM cana-5016 78 20 where𝐽𝑖 where𝐽𝑖 PUNCT cana-5016 78 21 being be AUX cana-5016 78 22 the the DET cana-5016 78 23 charge charge NOUN cana-5016 78 24 - - PUNCT cana-5016 78 25 current current ADJ cana-5016 78 26 density density NOUN cana-5016 78 27 that that PRON cana-5016 78 28 becomes become VERB cana-5016 78 29 ie ie ADV cana-5016 78 30 i i PRON cana-5016 78 31 uj uj VERB cana-5016 78 32 βˆ’ βˆ’ PROPN cana-5016 78 33 = = PROPN cana-5016 78 34 ( ( PUNCT cana-5016 78 35 e e X cana-5016 78 36 βˆ’ βˆ’ PROPN cana-5016 78 37   NOUN cana-5016 78 38 is be AUX cana-5016 78 39 the the DET cana-5016 78 40 proper proper ADJ cana-5016 78 41 charge charge NOUN cana-5016 78 42 density density NOUN cana-5016 78 43 ) ) PUNCT cana-5016 78 44 . . PUNCT cana-5016 79 1 in in ADP cana-5016 79 2 the the DET cana-5016 79 3 commoving commoving ADJ cana-5016 79 4 system system NOUN cana-5016 79 5 , , PUNCT cana-5016 79 6 we we PRON cana-5016 79 7 choose choose VERB cana-5016 79 8 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 79 9 = = PUNCT cana-5016 79 10 ( ( PUNCT cana-5016 79 11     SPACE cana-5016 79 12 0 0 NUM cana-5016 79 13 , , PUNCT cana-5016 79 14     SPACE cana-5016 79 15 0 0 NUM cana-5016 79 16 , , PUNCT cana-5016 79 17     SPACE cana-5016 79 18 0 0 NUM cana-5016 79 19 , , PUNCT cana-5016 79 20     SPACE cana-5016 79 21 β‹― β‹― PROPN cana-5016 79 22 , , PUNCT cana-5016 79 23 ( ( PUNCT cana-5016 79 24 𝑛 𝑛 PROPN cana-5016 80 1 + + X cana-5016 80 2 1)0 1)0 NUM cana-5016 80 3 , , PUNCT cana-5016 80 4 π‘ˆπ‘›+2 π‘ˆπ‘›+2 NOUN cana-5016 80 5 ) ) PUNCT cana-5016 80 6 πœ’π‘– πœ’π‘– NOUN cana-5016 80 7 = = SYM cana-5016 80 8 ( ( PUNCT cana-5016 80 9 πœ’1 πœ’1 PROPN cana-5016 80 10 , , PUNCT cana-5016 80 11     SPACE cana-5016 80 12 0 0 NUM cana-5016 80 13 , , PUNCT cana-5016 80 14     SPACE cana-5016 80 15 0 0 NUM cana-5016 80 16 , , PUNCT cana-5016 80 17     SPACE cana-5016 80 18 β‹― β‹― NOUN cana-5016 80 19     SPACE cana-5016 80 20 , , PUNCT cana-5016 80 21 0(𝑛 0(𝑛 X cana-5016 81 1 + + CCONJ cana-5016 81 2 1 1 NUM cana-5016 81 3 ) ) PUNCT cana-5016 81 4 ) ) PUNCT cana-5016 81 5 from from ADP cana-5016 81 6 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 81 7     SPACE cana-5016 81 8 π‘ˆπ‘– π‘ˆπ‘– PROPN cana-5016 81 9 = = PUNCT cana-5016 81 10 βˆ’πœ’π‘– βˆ’πœ’π‘– NOUN cana-5016 81 11     SPACE cana-5016 81 12 πœ’π‘– πœ’π‘– NOUN cana-5016 82 1 = = SYM cana-5016 82 2 1 1 NUM cana-5016 82 3 , , PUNCT cana-5016 82 4 we we PRON cana-5016 82 5 obtain obtain VERB cana-5016 82 6 π‘ˆ(𝑛+2 π‘ˆ(𝑛+2 PRON cana-5016 82 7 ) ) PUNCT cana-5016 82 8 = = SYM cana-5016 82 9 π‘’βˆ’πœˆ/2 π‘’βˆ’πœˆ/2 ADJ cana-5016 82 10 , , PUNCT cana-5016 82 11       SPACE cana-5016 82 12 πœ’1 πœ’1 PROPN cana-5016 82 13 = = PROPN cana-5016 82 14 π‘’βˆ’πœ†/2 π‘’βˆ’πœ†/2 PROPN cana-5016 82 15 . . PUNCT cana-5016 83 1 ( ( PUNCT cana-5016 83 2 10 10 NUM cana-5016 83 3 ) ) PUNCT cana-5016 83 4 the the DET cana-5016 83 5 non non ADJ cana-5016 83 6 - - ADJ cana-5016 83 7 vanishing vanishing ADJ cana-5016 83 8 components component NOUN cana-5016 83 9 of of ADP cana-5016 83 10 energy energy NOUN cana-5016 83 11 momentum momentum NOUN cana-5016 83 12 tensors tensor NOUN cana-5016 83 13 𝑇𝑗 𝑇𝑗 NOUN cana-5016 83 14 𝑖 𝑖 NOUN cana-5016 83 15 are be AUX cana-5016 83 16 =βˆ’====βˆ’= =βˆ’====βˆ’= ADJ cana-5016 83 17 + + X cana-5016 84 1 + + ADJ cana-5016 84 2 βŠ₯ βŠ₯ NOUN cana-5016 84 3 + + X cana-5016 84 4 + + CCONJ cana-5016 84 5 2n 2n NUM cana-5016 84 6 2n 2n NUM cana-5016 85 1 aa aa NOUN cana-5016 85 2 1n 1n NUM cana-5016 85 3 1n 1n NOUN cana-5016 85 4 a a DET cana-5016 85 5 3 3 NUM cana-5016 85 6 3 3 NUM cana-5016 85 7 a a DET cana-5016 85 8 2 2 NUM cana-5016 85 9 2r 2r NUM cana-5016 85 10 a a DET cana-5016 85 11 1 1 NUM cana-5016 85 12 1 1 NUM cana-5016 85 13 t t NOUN cana-5016 85 14 , , PUNCT cana-5016 85 15 pttt pttt NOUN cana-5016 85 16 , , PUNCT cana-5016 85 17 pt pt NOUN cana-5016 85 18   NOUN cana-5016 85 19 and and CCONJ cana-5016 85 20 21n 21n NOUN cana-5016 85 21 1n 1n NUM cana-5016 85 22 e e NOUN cana-5016 85 23 4 4 NUM cana-5016 85 24 4 4 NUM cana-5016 85 25 e e NOUN cana-5016 85 26 3 3 NUM cana-5016 85 27 3 3 NUM cana-5016 85 28 e e NOUN cana-5016 85 29 2 2 NUM cana-5016 85 30 2 2 NUM cana-5016 85 31 e e NOUN cana-5016 85 32 22n 22n X cana-5016 85 33 2n 2n NUM cana-5016 85 34 e e NOUN cana-5016 85 35 1 1 NUM cana-5016 85 36 1 1 NUM cana-5016 85 37 e e NOUN cana-5016 85 38 etttt etttt NOUN cana-5016 85 39 , , PUNCT cana-5016 85 40 ett ett PROPN cana-5016 85 41 βˆ’======= βˆ’======= PROPN cana-5016 86 1 + + CCONJ cana-5016 86 2 + + PUNCT cana-5016 86 3 + + CCONJ cana-5016 86 4 + + CCONJ cana-5016 86 5   NOUN cana-5016 86 6 . . PUNCT cana-5016 87 1 now now ADV cana-5016 87 2 let let VERB cana-5016 87 3 us we PRON cana-5016 87 4 tern tern VERB cana-5016 87 5 to to ADP cana-5016 87 6 the the DET cana-5016 87 7 gravitational gravitational ADJ cana-5016 87 8 field field NOUN cana-5016 87 9 equations equation NOUN cana-5016 87 10 . . PUNCT cana-5016 88 1 in in ADP cana-5016 88 2 bimetric bimetric ADJ cana-5016 88 3 theory theory NOUN cana-5016 88 4 of of ADP cana-5016 88 5 reletivity reletivity NOUN cana-5016 88 6 they they PRON cana-5016 88 7 have have VERB cana-5016 88 8 the the DET cana-5016 88 9 form form NOUN cana-5016 88 10 [ [ X cana-5016 88 11 rosen rosen PROPN cana-5016 88 12 , , PUNCT cana-5016 88 13 ( ( PUNCT cana-5016 88 14 1980 1980 NUM cana-5016 88 15 ) ) PUNCT cana-5016 88 16 ] ] PUNCT cana-5016 89 1 οƒ· οƒ· PROPN cana-5016 89 2 οƒΈ οƒΈ NUM cana-5016 89 3 οƒΆ οƒΆ PRON cana-5016 89 4   PROPN cana-5016 89 5   PROPN cana-5016 89 6   NOUN cana-5016 89 7 + + ADP cana-5016 89 8 ο°βˆ’=βˆ’βˆ’ο‚Ί ο°βˆ’=βˆ’βˆ’ο‚Ί ADJ cana-5016 89 9 e e X cana-5016 89 10 ij ij ADP cana-5016 89 11 a a DET cana-5016 89 12 ijijijijij ijijijijij NOUN cana-5016 89 13 tt8srg tt8srg ADP cana-5016 89 14 2 2 NUM cana-5016 89 15 1 1 NUM cana-5016 89 16 rg rg INTJ cana-5016 89 17 , , PUNCT cana-5016 89 18 ( ( PUNCT cana-5016 89 19 12 12 NUM cana-5016 89 20 ) ) PUNCT cana-5016 89 21 where where SCONJ cana-5016 89 22 the the DET cana-5016 89 23 additional additional ADJ cana-5016 89 24 term term NOUN cana-5016 89 25 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-5016 89 26 is be AUX cana-5016 89 27 given give VERB cana-5016 89 28 by by ADP cana-5016 89 29 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-5016 89 30 = = PROPN cana-5016 89 31 3 3 NUM cana-5016 89 32 π‘Ž2 π‘Ž2 NOUN cana-5016 89 33 ( ( PUNCT cana-5016 89 34 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5016 89 35 βˆ’ βˆ’ PROPN cana-5016 89 36 1 1 NUM cana-5016 89 37 2 2 NUM cana-5016 89 38 𝑔𝑖𝑗𝑔𝛼𝛽𝛾𝛼𝛽 𝑔𝑖𝑗𝑔𝛼𝛽𝛾𝛼𝛽 NOUN cana-5016 89 39 ) ) PUNCT cana-5016 89 40 . . PUNCT cana-5016 90 1 ( ( PUNCT cana-5016 90 2 13 13 NUM cana-5016 90 3 ) ) PUNCT cana-5016 90 4 if if SCONJ cana-5016 90 5 we we PRON cana-5016 90 6 take take VERB cana-5016 90 7 the the DET cana-5016 90 8 background background NOUN cana-5016 90 9 metric metric ADJ cana-5016 90 10 𝛾𝑖𝑗 𝛾𝑖𝑗 NOUN cana-5016 90 11 in in ADP cana-5016 90 12 a a DET cana-5016 90 13 higher high ADJ cana-5016 90 14 dimensional dimensional ADJ cana-5016 90 15 static static ADJ cana-5016 90 16 de de ADJ cana-5016 90 17 - - ADJ cana-5016 90 18 sitter sitter NOUN cana-5016 90 19 form form NOUN cana-5016 90 20 , , PUNCT cana-5016 90 21 the the DET cana-5016 90 22 line line NOUN cana-5016 90 23 element element NOUN cana-5016 90 24 in in ADP cana-5016 90 25 terms term NOUN cana-5016 90 26 of of ADP cana-5016 90 27 polar polar ADJ cana-5016 90 28 coordinates coordinate NOUN cana-5016 90 29 ( ( PUNCT cana-5016 90 30 π‘₯1 π‘₯1 NOUN cana-5016 90 31 , , PUNCT cana-5016 90 32 π‘₯2 π‘₯2 PROPN cana-5016 90 33 β‹― β‹― PROPN cana-5016 90 34 , , PUNCT cana-5016 90 35 π‘₯𝑛+1 π‘₯𝑛+1 PROPN cana-5016 90 36 , , PUNCT cana-5016 90 37     SPACE cana-5016 90 38 π‘₯𝑛+2 π‘₯𝑛+2 NUM cana-5016 90 39 ) ) PUNCT cana-5016 90 40 = = SYM cana-5016 90 41 ( ( PUNCT cana-5016 90 42 π‘Ÿ π‘Ÿ NOUN cana-5016 90 43 , , PUNCT cana-5016 90 44 πœƒ1 πœƒ1 VERB cana-5016 90 45 , , PUNCT cana-5016 90 46     SPACE cana-5016 90 47 πœƒ2 πœƒ2 PROPN cana-5016 90 48 , , PUNCT cana-5016 90 49     SPACE cana-5016 90 50 β‹― β‹― PROPN cana-5016 90 51 , , PUNCT cana-5016 90 52 πœƒπ‘› πœƒπ‘› NOUN cana-5016 90 53 , , PUNCT cana-5016 90 54     SPACE cana-5016 90 55 𝑑 𝑑 X cana-5016 90 56 ) ) PUNCT cana-5016 90 57 is be AUX cana-5016 90 58 given give VERB cana-5016 90 59 by by ADP cana-5016 90 60 π‘‘πœŽ2 π‘‘πœŽ2 NOUN cana-5016 90 61 = = SYM cana-5016 90 62 ( ( PUNCT cana-5016 90 63 1 1 NUM cana-5016 90 64 βˆ’ βˆ’ NUM cana-5016 90 65 π‘Ÿπ‘› π‘Ÿπ‘› ADP cana-5016 90 66 π‘Ž2 π‘Ž2 PROPN cana-5016 90 67 ) ) PUNCT cana-5016 90 68     SPACE cana-5016 90 69 𝑑𝑑2 𝑑𝑑2 NOUN cana-5016 90 70 βˆ’ βˆ’ PROPN cana-5016 90 71 ( ( PUNCT cana-5016 90 72 1 1 NUM cana-5016 90 73 βˆ’ βˆ’ NUM cana-5016 90 74 π‘Ÿπ‘› π‘Ÿπ‘› ADP cana-5016 90 75 π‘Ž2 π‘Ž2 PROPN cana-5016 90 76 ) ) PUNCT cana-5016 90 77 βˆ’1 βˆ’1 NOUN cana-5016 90 78 π‘‘π‘Ÿ2 π‘‘π‘Ÿ2 VERB cana-5016 90 79 βˆ’ βˆ’ PRON cana-5016 90 80     SPACE cana-5016 90 81 π‘Ÿ2𝑑𝛺2 π‘Ÿ2𝑑𝛺2 NUM cana-5016 90 82 . . PUNCT cana-5016 91 1 ( ( PUNCT cana-5016 91 2 14 14 NUM cana-5016 91 3 ) ) PUNCT cana-5016 91 4 for for ADP cana-5016 91 5 a a DET cana-5016 91 6 region region NOUN cana-5016 91 7 very very ADV cana-5016 91 8 small small ADJ cana-5016 91 9 as as SCONJ cana-5016 91 10 compared compare VERB cana-5016 91 11 to to ADP cana-5016 91 12 π‘Ž π‘Ž PROPN cana-5016 91 13 ( ( PUNCT cana-5016 91 14 i.e. i.e. X cana-5016 91 15 for for ADP cana-5016 91 16 π‘Ÿ π‘Ÿ NOUN cana-5016 91 17 < < X cana-5016 91 18 < < X cana-5016 91 19 π‘Ž π‘Ž NOUN cana-5016 91 20 ) ) PUNCT cana-5016 91 21 , , PUNCT cana-5016 91 22 this this DET cana-5016 91 23 line line NOUN cana-5016 91 24 element element NOUN cana-5016 91 25 has have VERB cana-5016 91 26 the the DET cana-5016 91 27 flat flat ADJ cana-5016 91 28 space space NOUN cana-5016 91 29 form form NOUN cana-5016 91 30 π‘‘πœŽ2 π‘‘πœŽ2 NOUN cana-5016 91 31 = = SYM cana-5016 91 32 𝑑𝑑2 𝑑𝑑2 NOUN cana-5016 91 33 βˆ’ βˆ’ PROPN cana-5016 91 34 π‘‘π‘Ÿ2 π‘‘π‘Ÿ2 VERB cana-5016 91 35 βˆ’ βˆ’ NOUN cana-5016 91 36 π‘Ÿ2𝑑𝛺2 π‘Ÿ2𝑑𝛺2 NUM cana-5016 91 37 . . PUNCT cana-5016 92 1 ( ( PUNCT cana-5016 92 2 15 15 NUM cana-5016 92 3 ) ) PUNCT cana-5016 92 4 ( ( PUNCT cana-5016 92 5 9 9 NUM cana-5016 92 6 ) ) PUNCT cana-5016 92 7 ( ( PUNCT cana-5016 92 8 11 11 NUM cana-5016 92 9 ) ) PUNCT cana-5016 92 10 communications communication NOUN cana-5016 92 11 on on ADP cana-5016 92 12 applied apply VERB cana-5016 92 13 nonlinear nonlinear ADJ cana-5016 92 14 analysis analysis NOUN cana-5016 92 15 issn issn NOUN cana-5016 92 16 : : PUNCT cana-5016 92 17 1074 1074 NUM cana-5016 92 18 - - PUNCT cana-5016 92 19 133x 133x NUM cana-5016 92 20 vol vol NOUN cana-5016 92 21 31 31 NUM cana-5016 92 22 no no NOUN cana-5016 92 23 . . PUNCT cana-5016 93 1 8s 8s PROPN cana-5016 93 2 ( ( PUNCT cana-5016 93 3 2024 2024 NUM cana-5016 93 4 ) ) PUNCT cana-5016 93 5 908 908 NUM cana-5016 93 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 93 7 let let VERB cana-5016 93 8 us we PRON cana-5016 93 9 consider consider VERB cana-5016 93 10 a a DET cana-5016 93 11 region region NOUN cana-5016 93 12 with with ADP cana-5016 93 13 π‘Ÿ π‘Ÿ NOUN cana-5016 93 14 < < X cana-5016 93 15 < < X cana-5016 93 16 π‘Ž π‘Ž NOUN cana-5016 93 17 and and CCONJ cana-5016 93 18 neglect neglect NOUN cana-5016 93 19 the the DET cana-5016 93 20 terms term NOUN cana-5016 93 21 , , PUNCT cana-5016 93 22 which which PRON cana-5016 93 23 are be AUX cana-5016 93 24 small small ADJ cana-5016 93 25 throughout throughout ADP cana-5016 93 26 this this DET cana-5016 93 27 region region NOUN cana-5016 93 28 , , PUNCT cana-5016 93 29 we we PRON cana-5016 93 30 can can AUX cana-5016 93 31 write write VERB cana-5016 93 32 the the DET cana-5016 93 33 non non ADJ cana-5016 93 34 - - ADJ cana-5016 93 35 vanishing vanishing ADJ cana-5016 93 36 components component NOUN cana-5016 93 37 of of ADP cana-5016 93 38 𝑆𝑖 𝑆𝑖 PROPN cana-5016 93 39 𝑗 𝑗 NOUN cana-5016 93 40 in in ADP cana-5016 93 41 higher high ADJ cana-5016 93 42 dimensions dimension NOUN cana-5016 93 43 ( ( PUNCT cana-5016 93 44 falik falik PROPN cana-5016 93 45 and and CCONJ cana-5016 93 46 rosen rosen PROPN cana-5016 93 47 , , PUNCT cana-5016 93 48 1980 1980 NUM cana-5016 93 49 ) ) PUNCT cana-5016 93 50 βˆ’π‘†1 βˆ’π‘†1 ADV cana-5016 94 1 1 1 NUM cana-5016 94 2 = = SYM cana-5016 94 3 βˆ’π‘†2 βˆ’π‘†2 NOUN cana-5016 94 4 2 2 NUM cana-5016 94 5     SPACE cana-5016 94 6 = = VERB cana-5016 94 7     SPACE cana-5016 94 8 βˆ’π‘†3 βˆ’π‘†3 VERB cana-5016 94 9 3 3 NUM cana-5016 94 10 = = SYM cana-5016 94 11 β‹― β‹― NOUN cana-5016 94 12 = = SYM cana-5016 94 13 βˆ’π‘†π‘›+1 βˆ’π‘†π‘›+1 NOUN cana-5016 94 14 𝑛+1 𝑛+1 PROPN cana-5016 94 15 = = SYM cana-5016 94 16 𝑆𝑛+2 𝑆𝑛+2 NOUN cana-5016 94 17 𝑛+2 𝑛+2 NOUN cana-5016 94 18 = = SYM cana-5016 94 19 3 3 NUM cana-5016 94 20 2π‘Ž 2π‘Ž NUM cana-5016 94 21 π‘’βˆ’πœˆ. π‘’βˆ’πœˆ. X cana-5016 94 22 ( ( PUNCT cana-5016 94 23 16 16 NUM cana-5016 94 24 ) ) PUNCT cana-5016 94 25 rosen rosen PROPN cana-5016 94 26 ’s ’s PART cana-5016 94 27 ( ( PUNCT cana-5016 94 28 1980 1980 NUM cana-5016 94 29 ) ) PUNCT cana-5016 94 30 bimetric bimetric ADJ cana-5016 94 31 field field NOUN cana-5016 94 32 equations equation NOUN cana-5016 94 33 given give VERB cana-5016 94 34 by by ADP cana-5016 94 35 equation equation NOUN cana-5016 94 36 ( ( PUNCT cana-5016 94 37 12 12 NUM cana-5016 94 38 ) ) PUNCT cana-5016 94 39 for for ADP cana-5016 94 40 the the PRON cana-5016 94 41 for for ADP cana-5016 94 42 the the DET cana-5016 94 43 line line NOUN cana-5016 94 44 - - PUNCT cana-5016 94 45 element element NOUN cana-5016 94 46 ( ( PUNCT cana-5016 94 47 2 2 NUM cana-5016 94 48 ) ) PUNCT cana-5016 94 49 ( ( PUNCT cana-5016 94 50 for for ADP cana-5016 94 51 π‘Ÿ π‘Ÿ PRON cana-5016 94 52 < < X cana-5016 94 53 < < X cana-5016 94 54 π‘Ž π‘Ž X cana-5016 94 55 ) ) PUNCT cana-5016 94 56 can can AUX cana-5016 94 57 be be AUX cana-5016 94 58 written write VERB cana-5016 94 59 as as ADP cana-5016 94 60 βˆ’π‘’βˆ’πœ† βˆ’π‘’βˆ’πœ† PROPN cana-5016 94 61 [ [ PUNCT cana-5016 94 62 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 94 63 ) ) PUNCT cana-5016 94 64 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 95 1 βˆ’ βˆ’ NUM cana-5016 96 1 π‘›πœ†β€² π‘›πœ†β€² NOUN cana-5016 96 2 2π‘Ÿ 2π‘Ÿ NOUN cana-5016 96 3 ] ] PUNCT cana-5016 97 1 + + PUNCT cana-5016 97 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 97 3 ) ) PUNCT cana-5016 97 4 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 98 1 = = PUNCT cana-5016 99 1 βˆ’ βˆ’ PROPN cana-5016 99 2 3 3 NUM cana-5016 99 3 2π‘Ž2 2π‘Ž2 NUM cana-5016 99 4 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 99 5 + + X cana-5016 99 6 .8πœ‹πœŒ .8πœ‹πœŒ PROPN cana-5016 100 1 + + CCONJ cana-5016 100 2 𝐸2 𝐸2 ADJ cana-5016 100 3 ( ( PUNCT cana-5016 100 4 17 17 NUM cana-5016 100 5 ) ) PUNCT cana-5016 100 6 βˆ’π‘’βˆ’πœ† βˆ’π‘’βˆ’πœ† PROPN cana-5016 100 7 [ [ PUNCT cana-5016 100 8 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 100 9 ) ) PUNCT cana-5016 100 10 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 101 1 + + CCONJ cana-5016 101 2 π‘›πœˆβ€² π‘›πœˆβ€² VERB cana-5016 101 3 2π‘Ÿ 2π‘Ÿ NUM cana-5016 101 4 ] ] PUNCT cana-5016 102 1 + + PUNCT cana-5016 102 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 102 3 ) ) PUNCT cana-5016 102 4 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 103 1 = = SYM cana-5016 103 2 3 3 NUM cana-5016 103 3 2π‘Ž2 2π‘Ž2 NUM cana-5016 103 4 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 103 5 βˆ’ βˆ’ PROPN cana-5016 103 6 8πœ‹π‘ƒπ‘Ÿ 8πœ‹π‘ƒπ‘Ÿ NOUN cana-5016 103 7 + + CCONJ cana-5016 103 8 𝐸2 𝐸2 ADJ cana-5016 103 9 ( ( PUNCT cana-5016 103 10 18 18 NUM cana-5016 103 11 ) ) PUNCT cana-5016 103 12 π‘’βˆ’πœ† π‘’βˆ’πœ† NOUN cana-5016 103 13 [ [ PUNCT cana-5016 103 14 πœˆβ€³ πœˆβ€³ X cana-5016 103 15 2 2 NUM cana-5016 103 16 + + CCONJ cana-5016 103 17 πœˆβ€²2 πœˆβ€²2 VERB cana-5016 103 18 4 4 NUM cana-5016 103 19 βˆ’ βˆ’ NOUN cana-5016 103 20 ( ( PUNCT cana-5016 103 21 𝑛 𝑛 PROPN cana-5016 103 22 βˆ’ βˆ’ PROPN cana-5016 103 23 1)(πœ†β€² 1)(πœ†β€² NUM cana-5016 103 24 βˆ’ βˆ’ PROPN cana-5016 103 25 πœˆβ€² πœˆβ€² NUM cana-5016 103 26 ) ) PUNCT cana-5016 104 1 2π‘Ÿ 2π‘Ÿ NOUN cana-5016 104 2 βˆ’ βˆ’ NOUN cana-5016 104 3 πœ†β€²πœˆβ€² πœ†β€²πœˆβ€² VERB cana-5016 104 4 4 4 NUM cana-5016 104 5 + + CCONJ cana-5016 104 6 ( ( PUNCT cana-5016 104 7 𝑛 𝑛 PRON cana-5016 104 8 βˆ’ βˆ’ NOUN cana-5016 104 9 1)(𝑛 1)(𝑛 NUM cana-5016 104 10 βˆ’ βˆ’ NOUN cana-5016 104 11 2 2 NUM cana-5016 104 12 ) ) PUNCT cana-5016 104 13 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 104 14 ] ] PUNCT cana-5016 105 1 βˆ’ βˆ’ PROPN cana-5016 105 2 ( ( PUNCT cana-5016 105 3 𝑛 𝑛 PROPN cana-5016 105 4 βˆ’ βˆ’ NOUN cana-5016 105 5 1)(𝑛 1)(𝑛 NUM cana-5016 105 6 βˆ’ βˆ’ NOUN cana-5016 105 7 2 2 NUM cana-5016 105 8 ) ) PUNCT cana-5016 105 9 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 105 10                   SPACE cana-5016 105 11 = = SYM cana-5016 106 1 βˆ’ βˆ’ PROPN cana-5016 106 2 3 3 NUM cana-5016 106 3 2π‘Ž2 2π‘Ž2 NUM cana-5016 106 4 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 106 5 + + CCONJ cana-5016 106 6 8πœ‹π‘ƒβŠ₯ 8πœ‹π‘ƒβŠ₯ NUM cana-5016 106 7 + + CCONJ cana-5016 106 8 𝐸2 𝐸2 ADJ cana-5016 106 9 , , PUNCT cana-5016 106 10 ( ( PUNCT cana-5016 106 11 19 19 NUM cana-5016 106 12 ) ) PUNCT cana-5016 106 13 where where SCONJ cana-5016 106 14 a a DET cana-5016 106 15 prime prime ADJ cana-5016 106 16 denotes denote VERB cana-5016 106 17 a a DET cana-5016 106 18 derivative derivative NOUN cana-5016 106 19 with with ADP cana-5016 106 20 respect respect NOUN cana-5016 106 21 to to ADP cana-5016 106 22 π‘Ÿ. π‘Ÿ. NOUN cana-5016 106 23 we we PRON cana-5016 106 24 now now ADV cana-5016 106 25 define define VERB cana-5016 106 26 the the DET cana-5016 106 27 effective effective ADJ cana-5016 106 28 density density NOUN cana-5016 106 29 and and CCONJ cana-5016 106 30 pressures pressure NOUN cana-5016 106 31 πœŒπ‘šπ‘’ πœŒπ‘šπ‘’ ADV cana-5016 106 32     SPACE cana-5016 106 33 , , PUNCT cana-5016 106 34       SPACE cana-5016 106 35 π‘ƒπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘’ PROPN cana-5016 106 36 and and CCONJ cana-5016 106 37 𝑃βŠ₯𝑒 𝑃βŠ₯𝑒 PROPN cana-5016 106 38 ( ( PUNCT cana-5016 106 39 harpaz harpaz PROPN cana-5016 106 40 and and CCONJ cana-5016 106 41 rosen rosen PROPN cana-5016 106 42 , , PUNCT cana-5016 106 43 1985 1985 NUM cana-5016 106 44 ) ) PUNCT cana-5016 106 45 as as SCONJ cana-5016 106 46 πœŒπ‘šπ‘’ πœŒπ‘šπ‘’ PRON cana-5016 106 47 = = SYM cana-5016 106 48 πœŒπ‘š πœŒπ‘š NOUN cana-5016 106 49 βˆ’ βˆ’ NUM cana-5016 106 50 3 3 NUM cana-5016 106 51 16πœ‹π‘Ž2 16πœ‹π‘Ž2 NUM cana-5016 106 52 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 106 53 , , PUNCT cana-5016 106 54         SPACE cana-5016 106 55 π‘ƒπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘’ PROPN cana-5016 106 56 = = PRON cana-5016 106 57 π‘ƒπ‘Ÿ π‘ƒπ‘Ÿ PROPN cana-5016 106 58 βˆ’ βˆ’ PROPN cana-5016 106 59 3 3 NUM cana-5016 106 60 16πœ‹π‘Ž2 16πœ‹π‘Ž2 NUM cana-5016 106 61 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 106 62 and and CCONJ cana-5016 106 63 𝑃βŠ₯𝑒 𝑃βŠ₯𝑒 PROPN cana-5016 106 64 = = PUNCT cana-5016 106 65 𝑃βŠ₯ 𝑃βŠ₯ VERB cana-5016 106 66 βˆ’ βˆ’ PROPN cana-5016 106 67 3 3 NUM cana-5016 106 68 16πœ‹π‘Ž2 16πœ‹π‘Ž2 NUM cana-5016 106 69 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 106 70 , , PUNCT cana-5016 106 71 so so SCONJ cana-5016 106 72 that that SCONJ cana-5016 106 73 the the DET cana-5016 106 74 field field NOUN cana-5016 106 75 equations equation NOUN cana-5016 106 76 ( ( PUNCT cana-5016 106 77 17 17 NUM cana-5016 106 78 ) ) PUNCT cana-5016 106 79 – – PUNCT cana-5016 106 80 ( ( PUNCT cana-5016 106 81 19 19 NUM cana-5016 106 82 ) ) PUNCT cana-5016 106 83 take take VERB cana-5016 106 84 the the DET cana-5016 106 85 form form NOUN cana-5016 106 86 βˆ’π‘’βˆ’πœ† βˆ’π‘’βˆ’πœ† PROPN cana-5016 106 87 [ [ PUNCT cana-5016 106 88 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 106 89 ) ) PUNCT cana-5016 106 90 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 106 91 βˆ’ βˆ’ NUM cana-5016 106 92 π‘›πœ†β€² π‘›πœ†β€² NOUN cana-5016 106 93 2π‘Ÿ 2π‘Ÿ NOUN cana-5016 106 94 ] ] PUNCT cana-5016 107 1 + + PUNCT cana-5016 107 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 107 3 ) ) PUNCT cana-5016 107 4 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 108 1 = = SYM cana-5016 108 2 8πœ‹πœŒπ‘šπ‘’ 8πœ‹πœŒπ‘šπ‘’ NUM cana-5016 109 1 + + CCONJ cana-5016 109 2 𝐸2 𝐸2 PROPN cana-5016 109 3 ( ( PUNCT cana-5016 109 4 21 21 NUM cana-5016 109 5 ) ) PUNCT cana-5016 109 6 βˆ’π‘’βˆ’πœ† βˆ’π‘’βˆ’πœ† PROPN cana-5016 109 7 [ [ PUNCT cana-5016 109 8 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 109 9 ) ) PUNCT cana-5016 109 10 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 110 1 + + CCONJ cana-5016 110 2 π‘›πœˆβ€² π‘›πœˆβ€² VERB cana-5016 110 3 2π‘Ÿ 2π‘Ÿ NUM cana-5016 110 4 ] ] PUNCT cana-5016 111 1 + + PUNCT cana-5016 111 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 111 3 ) ) PUNCT cana-5016 111 4 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 112 1 = = PUNCT cana-5016 112 2 βˆ’8πœ‹π‘ƒπ‘Ÿπ‘’ βˆ’8πœ‹π‘ƒπ‘Ÿπ‘’ PROPN cana-5016 112 3 + + CCONJ cana-5016 112 4 𝐸2 𝐸2 PROPN cana-5016 112 5 ( ( PUNCT cana-5016 112 6 22 22 NUM cana-5016 112 7 ) ) PUNCT cana-5016 112 8 π‘’βˆ’πœ† π‘’βˆ’πœ† NOUN cana-5016 112 9 [ [ PUNCT cana-5016 112 10 πœˆβ€³ πœˆβ€³ X cana-5016 112 11 2 2 NUM cana-5016 112 12 + + CCONJ cana-5016 112 13 πœˆβ€²2 πœˆβ€²2 VERB cana-5016 112 14 4 4 NUM cana-5016 112 15 βˆ’ βˆ’ NOUN cana-5016 112 16 ( ( PUNCT cana-5016 112 17 𝑛 𝑛 PROPN cana-5016 112 18 βˆ’ βˆ’ PROPN cana-5016 112 19 1)(πœ†β€² 1)(πœ†β€² NUM cana-5016 112 20 βˆ’ βˆ’ PROPN cana-5016 112 21 πœˆβ€² πœˆβ€² NUM cana-5016 112 22 ) ) PUNCT cana-5016 112 23 2π‘Ÿ 2π‘Ÿ NOUN cana-5016 112 24 βˆ’ βˆ’ NOUN cana-5016 112 25 πœ†β€²πœˆβ€² πœ†β€²πœˆβ€² VERB cana-5016 112 26 4 4 NUM cana-5016 112 27 + + CCONJ cana-5016 112 28 ( ( PUNCT cana-5016 112 29 𝑛 𝑛 PRON cana-5016 112 30 βˆ’ βˆ’ NOUN cana-5016 112 31 1)(𝑛 1)(𝑛 NUM cana-5016 112 32 βˆ’ βˆ’ NOUN cana-5016 112 33 2 2 NUM cana-5016 112 34 ) ) PUNCT cana-5016 112 35 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 112 36 ] ] PUNCT cana-5016 113 1 βˆ’ βˆ’ PROPN cana-5016 113 2 ( ( PUNCT cana-5016 113 3 𝑛 𝑛 PROPN cana-5016 113 4 βˆ’ βˆ’ NOUN cana-5016 113 5 1)(𝑛 1)(𝑛 NUM cana-5016 113 6 βˆ’ βˆ’ NOUN cana-5016 113 7 2 2 NUM cana-5016 113 8 ) ) PUNCT cana-5016 113 9 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 113 10                   SPACE cana-5016 113 11 = = SYM cana-5016 113 12 8πœ‹π‘ƒβŠ₯𝑒 8πœ‹π‘ƒβŠ₯𝑒 PROPN cana-5016 113 13 + + CCONJ cana-5016 113 14 𝐸2 𝐸2 ADJ cana-5016 113 15 . . PUNCT cana-5016 114 1 ( ( PUNCT cana-5016 114 2 23 23 NUM cana-5016 114 3 ) ) PUNCT cana-5016 114 4 these these DET cana-5016 114 5 equations equation NOUN cana-5016 114 6 look look VERB cana-5016 114 7 like like ADP cana-5016 114 8 the the DET cana-5016 114 9 usual usual ADJ cana-5016 114 10 einstein einstein PROPN cana-5016 114 11 equations equation NOUN cana-5016 114 12 with with ADP cana-5016 114 13 πœŒπ‘š πœŒπ‘š PROPN cana-5016 114 14 , , PUNCT cana-5016 114 15 π‘π‘Ÿ π‘π‘Ÿ PROPN cana-5016 114 16 and and CCONJ cana-5016 114 17 𝑝βŠ₯ 𝑝βŠ₯ PROPN cana-5016 114 18 replaced replace VERB cana-5016 114 19 by by ADP cana-5016 114 20 πœŒπ‘šπ‘’ πœŒπ‘šπ‘’ PRON cana-5016 114 21 , , PUNCT cana-5016 114 22       SPACE cana-5016 114 23 π‘π‘Ÿπ‘’ π‘π‘Ÿπ‘’ NOUN cana-5016 114 24 and and CCONJ cana-5016 114 25 𝑝βŠ₯𝑒 𝑝βŠ₯𝑒 PROPN cana-5016 114 26 respectively respectively ADV cana-5016 114 27 . . PUNCT cana-5016 115 1 it it PRON cana-5016 115 2 is be AUX cana-5016 115 3 very very ADV cana-5016 115 4 difficult difficult ADJ cana-5016 115 5 to to PART cana-5016 115 6 obtain obtain VERB cana-5016 115 7 the the DET cana-5016 115 8 solution solution NOUN cana-5016 115 9 of of ADP cana-5016 115 10 equations equation NOUN cana-5016 115 11 ( ( PUNCT cana-5016 115 12 21)-(23 21)-(23 NOUN cana-5016 115 13 ) ) PUNCT cana-5016 115 14 due due ADP cana-5016 115 15 to to ADP cana-5016 115 16 the the DET cana-5016 115 17 non non NOUN cana-5016 115 18 - - NOUN cana-5016 115 19 linearity linearity NOUN cana-5016 115 20 of of ADP cana-5016 115 21 the the DET cana-5016 115 22 field field NOUN cana-5016 115 23 equations equation NOUN cana-5016 115 24 and and CCONJ cana-5016 115 25 therefore therefore ADV cana-5016 115 26 one one NUM cana-5016 115 27 has have VERB cana-5016 115 28 to to PART cana-5016 115 29 make make VERB cana-5016 115 30 certain certain ADJ cana-5016 115 31 simplifying simplifying NOUN cana-5016 115 32 assumption assumption NOUN cana-5016 115 33 to to PART cana-5016 115 34 derive derive VERB cana-5016 115 35 the the DET cana-5016 115 36 useful useful ADJ cana-5016 115 37 results result NOUN cana-5016 115 38 . . PUNCT cana-5016 116 1 3 3 X cana-5016 116 2 . . X cana-5016 116 3 conformal conformal ADJ cana-5016 116 4 motions motion NOUN cana-5016 116 5 and and CCONJ cana-5016 116 6 solutions solution NOUN cana-5016 116 7 of of ADP cana-5016 116 8 field field NOUN cana-5016 116 9 equations equation NOUN cana-5016 116 10 in in ADP cana-5016 116 11 this this DET cana-5016 116 12 section section NOUN cana-5016 116 13 , , PUNCT cana-5016 116 14 we we PRON cana-5016 116 15 assume assume VERB cana-5016 116 16 that that SCONJ cana-5016 116 17 the the DET cana-5016 116 18 physical physical ADJ cana-5016 116 19 metric metric NOUN cana-5016 116 20 ( ( PUNCT cana-5016 116 21 2 2 NUM cana-5016 116 22 ) ) PUNCT cana-5016 116 23 admits admit VERB cana-5016 116 24 a a DET cana-5016 116 25 one one NUM cana-5016 116 26 - - PUNCT cana-5016 116 27 parameter parameter NOUN cana-5016 116 28 group group NOUN cana-5016 116 29 of of ADP cana-5016 116 30 conformal conformal ADJ cana-5016 116 31 motions motion NOUN cana-5016 116 32 and and CCONJ cana-5016 116 33 obtained obtain VERB cana-5016 116 34 solution solution NOUN cana-5016 116 35 of of ADP cana-5016 116 36 the the DET cana-5016 116 37 field field NOUN cana-5016 116 38 equations equation NOUN cana-5016 116 39 for for ADP cana-5016 116 40 static static ADJ cana-5016 116 41 and and CCONJ cana-5016 116 42 spherically spherically NOUN cana-5016 116 43 symmetric symmetric ADJ cana-5016 116 44 fluid fluid ADJ cana-5016 116 45 distributions distribution NOUN cana-5016 116 46 of of ADP cana-5016 116 47 anisotropic anisotropic NOUN cana-5016 116 48 matter matter NOUN cana-5016 116 49 . . PUNCT cana-5016 117 1 the the DET cana-5016 117 2 field field NOUN cana-5016 117 3 equations equation NOUN cana-5016 117 4 ( ( PUNCT cana-5016 117 5 21)-(23 21)-(23 NOUN cana-5016 117 6 ) ) PUNCT cana-5016 117 7 resulting result VERB cana-5016 117 8 in in ADP cana-5016 117 9 the the DET cana-5016 117 10 new new ADJ cana-5016 117 11 form form NOUN cana-5016 117 12 ( ( PUNCT cana-5016 117 13 20 20 NUM cana-5016 117 14 ) ) PUNCT cana-5016 117 15 communications communication NOUN cana-5016 117 16 on on ADP cana-5016 117 17 applied apply VERB cana-5016 117 18 nonlinear nonlinear ADJ cana-5016 117 19 analysis analysis NOUN cana-5016 117 20 issn issn NOUN cana-5016 117 21 : : PUNCT cana-5016 117 22 1074 1074 NUM cana-5016 117 23 - - PUNCT cana-5016 117 24 133x 133x NUM cana-5016 117 25 vol vol NOUN cana-5016 117 26 31 31 NUM cana-5016 117 27 no no NOUN cana-5016 117 28 . . PUNCT cana-5016 118 1 8s 8s PROPN cana-5016 118 2 ( ( PUNCT cana-5016 118 3 2024 2024 NUM cana-5016 118 4 ) ) PUNCT cana-5016 118 5 909 909 NUM cana-5016 118 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 118 7 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 118 8 ) ) PUNCT cana-5016 118 9 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 119 1 [ [ X cana-5016 119 2 1 1 NUM cana-5016 119 3 βˆ’ βˆ’ PROPN cana-5016 119 4 πœ“2 πœ“2 NOUN cana-5016 119 5 𝐢3 𝐢3 NOUN cana-5016 119 6 2 2 NUM cana-5016 119 7 ] ] PUNCT cana-5016 119 8 βˆ’ βˆ’ PROPN cana-5016 119 9 π‘›πœ“πœ“β€² π‘›πœ“πœ“β€² NOUN cana-5016 119 10 𝐢3 𝐢3 PROPN cana-5016 119 11 2π‘Ÿ 2π‘Ÿ PROPN cana-5016 119 12 = = SYM cana-5016 119 13 8πœ‹πœŒπ‘’ 8πœ‹πœŒπ‘’ PROPN cana-5016 119 14 + + CCONJ cana-5016 119 15 𝐸2 𝐸2 ADJ cana-5016 119 16 , , PUNCT cana-5016 119 17 ( ( PUNCT cana-5016 119 18 24 24 NUM cana-5016 119 19 ) ) PUNCT cana-5016 119 20 βˆ’ βˆ’ PROPN cana-5016 119 21 π‘›πœ“2 π‘›πœ“2 PROPN cana-5016 119 22 𝐢3 𝐢3 PROPN cana-5016 119 23 2π‘Ÿ2 2π‘Ÿ2 PROPN cana-5016 120 1 [ [ X cana-5016 120 2 1 1 NUM cana-5016 120 3 βˆ’ βˆ’ PROPN cana-5016 120 4 ( ( PUNCT cana-5016 120 5 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-5016 120 6 ) ) PUNCT cana-5016 120 7 2 2 NUM cana-5016 120 8 ] ] PUNCT cana-5016 120 9 + + NUM cana-5016 120 10 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 120 11 ) ) PUNCT cana-5016 120 12 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 120 13 = = SYM cana-5016 120 14 8πœ‹π‘ƒπ‘Ÿπ‘’ 8πœ‹π‘ƒπ‘Ÿπ‘’ NUM cana-5016 120 15 + + CCONJ cana-5016 120 16 𝐸2 𝐸2 ADJ cana-5016 120 17 , , PUNCT cana-5016 120 18 ( ( PUNCT cana-5016 120 19 25 25 NUM cana-5016 120 20 ) ) PUNCT cana-5016 121 1 π‘›πœ“πœ“β€² π‘›πœ“πœ“β€² NOUN cana-5016 121 2 π‘ŸπΆ3 π‘ŸπΆ3 NOUN cana-5016 121 3 2 2 NUM cana-5016 122 1 + + CCONJ cana-5016 122 2 𝑛(π‘›βˆ’1)πœ“2 𝑛(π‘›βˆ’1)πœ“2 NUM cana-5016 122 3 2π‘Ÿ2𝐢3 2π‘Ÿ2𝐢3 NUM cana-5016 122 4 2 2 NUM cana-5016 122 5 βˆ’ βˆ’ NOUN cana-5016 122 6 ( ( PUNCT cana-5016 122 7 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 122 8 ) ) PUNCT cana-5016 122 9 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 123 1 = = SYM cana-5016 123 2 8πœ‹π‘ƒβŠ₯𝑒 8πœ‹π‘ƒβŠ₯𝑒 PROPN cana-5016 123 3 + + CCONJ cana-5016 123 4 𝐸2 𝐸2 ADJ cana-5016 123 5 , , PUNCT cana-5016 123 6 ( ( PUNCT cana-5016 123 7 26 26 NUM cana-5016 123 8 ) ) PUNCT cana-5016 123 9 we we PRON cana-5016 123 10 now now ADV cana-5016 123 11 define define VERB cana-5016 123 12 a a DET cana-5016 123 13 function function NOUN cana-5016 123 14 π›₯ π›₯ PROPN cana-5016 123 15 , , PUNCT cana-5016 123 16 as as ADP cana-5016 123 17 a a DET cana-5016 123 18 measure measure NOUN cana-5016 123 19 of of ADP cana-5016 123 20 anisotropy anisotropy NOUN cana-5016 123 21 , , PUNCT cana-5016 123 22 such such ADJ cana-5016 123 23 that that SCONJ cana-5016 123 24 π›₯ π›₯ PROPN cana-5016 123 25 = = NOUN cana-5016 123 26 4πœ‹(𝑃βŠ₯𝑒 4πœ‹(𝑃βŠ₯𝑒 NUM cana-5016 123 27 βˆ’ βˆ’ PROPN cana-5016 123 28 π‘ƒπ‘Ÿπ‘’ π‘ƒπ‘Ÿπ‘’ PROPN cana-5016 123 29 ) ) PUNCT cana-5016 123 30 . . PUNCT cana-5016 124 1 ( ( PUNCT cana-5016 124 2 27 27 NUM cana-5016 124 3 ) ) PUNCT cana-5016 124 4 also also ADV cana-5016 124 5 , , PUNCT cana-5016 124 6 if if SCONJ cana-5016 124 7 we we PRON cana-5016 124 8 take take VERB cana-5016 124 9 𝑋 𝑋 NOUN cana-5016 124 10 = = SYM cana-5016 124 11 πœ“2 πœ“2 NOUN cana-5016 124 12 𝐢3 𝐢3 NOUN cana-5016 124 13 2 2 NUM cana-5016 124 14 , , PUNCT cana-5016 124 15 then then ADV cana-5016 124 16 in in ADP cana-5016 124 17 terms term NOUN cana-5016 124 18 of of ADP cana-5016 124 19 the the DET cana-5016 124 20 function function NOUN cana-5016 124 21 defined define VERB cana-5016 124 22 in in ADP cana-5016 124 23 ( ( PUNCT cana-5016 124 24 27 27 NUM cana-5016 124 25 ) ) PUNCT cana-5016 124 26 , , PUNCT cana-5016 124 27 the the DET cana-5016 124 28 equations equation NOUN cana-5016 124 29 ( ( PUNCT cana-5016 124 30 24 24 NUM cana-5016 124 31 ) ) PUNCT cana-5016 124 32 – – PUNCT cana-5016 124 33 ( ( PUNCT cana-5016 124 34 26 26 NUM cana-5016 124 35 ) ) PUNCT cana-5016 124 36 reduces reduce VERB cana-5016 124 37 to to PART cana-5016 124 38 : : PUNCT cana-5016 124 39 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 124 40 ) ) PUNCT cana-5016 124 41 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 125 1 βˆ’ βˆ’ PROPN cana-5016 126 1 𝑛𝑋 𝑛𝑋 PROPN cana-5016 126 2 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 127 1 + + CCONJ cana-5016 127 2 𝑛𝑋′ 𝑛𝑋′ PROPN cana-5016 127 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 127 4 βˆ’ βˆ’ PROPN cana-5016 127 5 ( ( PUNCT cana-5016 127 6 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 127 7 ) ) PUNCT cana-5016 127 8 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 128 1 βˆ’ βˆ’ NOUN cana-5016 128 2 π›₯ π›₯ PROPN cana-5016 128 3 = = SYM cana-5016 128 4 𝐸2 𝐸2 PROPN cana-5016 128 5 ( ( PUNCT cana-5016 128 6 28 28 NUM cana-5016 128 7 ) ) PUNCT cana-5016 128 8 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 128 9 ) ) PUNCT cana-5016 128 10 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 129 1 βˆ’ βˆ’ PROPN cana-5016 129 2 3𝑛𝑋′ 3𝑛𝑋′ NUM cana-5016 129 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 129 4 βˆ’ βˆ’ PROPN cana-5016 129 5 𝑛(π‘›βˆ’2)𝑋 𝑛(π‘›βˆ’2)𝑋 ADJ cana-5016 129 6 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 130 1 βˆ’ βˆ’ NOUN cana-5016 130 2 ( ( PUNCT cana-5016 130 3 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 130 4 ) ) PUNCT cana-5016 130 5 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 131 1 + + CCONJ cana-5016 131 2 π›₯ π›₯ PROPN cana-5016 131 3 = = SYM cana-5016 131 4 8πœ‹πœŒπ‘šπ‘’ 8πœ‹πœŒπ‘šπ‘’ NUM cana-5016 131 5 ( ( PUNCT cana-5016 131 6 29 29 NUM cana-5016 131 7 ) ) PUNCT cana-5016 131 8 𝑛𝑋 𝑛𝑋 PROPN cana-5016 131 9 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 132 1 βˆ’ βˆ’ PROPN cana-5016 132 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 132 3 ) ) PUNCT cana-5016 132 4 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 133 1 + + CCONJ cana-5016 133 2 𝑛𝑋′ 𝑛𝑋′ PROPN cana-5016 133 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 133 4 βˆ’ βˆ’ PROPN cana-5016 133 5 ( ( PUNCT cana-5016 133 6 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 133 7 ) ) PUNCT cana-5016 133 8 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 134 1 βˆ’ βˆ’ NOUN cana-5016 134 2 π›₯ π›₯ NOUN cana-5016 134 3 = = NOUN cana-5016 134 4 8πœ‹π‘ƒπ‘Ÿπ‘’ 8πœ‹π‘ƒπ‘Ÿπ‘’ NUM cana-5016 134 5 . . PUNCT cana-5016 135 1 ( ( PUNCT cana-5016 135 2 30 30 NUM cana-5016 135 3 ) ) PUNCT cana-5016 135 4 from from ADP cana-5016 135 5 which which PRON cana-5016 135 6 we we PRON cana-5016 135 7 obtain obtain VERB cana-5016 135 8 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 135 9 ) ) PUNCT cana-5016 135 10 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 136 1 βˆ’ βˆ’ PROPN cana-5016 137 1 𝑛𝑋 𝑛𝑋 PROPN cana-5016 137 2 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 138 1 + + CCONJ cana-5016 138 2 𝑛𝑋′ 𝑛𝑋′ PROPN cana-5016 138 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 138 4 βˆ’ βˆ’ PROPN cana-5016 138 5 ( ( PUNCT cana-5016 138 6 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 138 7 ) ) PUNCT cana-5016 138 8 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 139 1 βˆ’ βˆ’ NOUN cana-5016 139 2 π›₯ π›₯ PROPN cana-5016 139 3 = = SYM cana-5016 139 4 𝐸2 𝐸2 PROPN cana-5016 139 5 ( ( PUNCT cana-5016 139 6 31 31 NUM cana-5016 139 7 ) ) PUNCT cana-5016 139 8 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 139 9 ) ) PUNCT cana-5016 139 10 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 140 1 βˆ’ βˆ’ PROPN cana-5016 140 2 3𝑛𝑋′ 3𝑛𝑋′ NUM cana-5016 140 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 140 4 βˆ’ βˆ’ PROPN cana-5016 140 5 𝑛(π‘›βˆ’2)𝑋 𝑛(π‘›βˆ’2)𝑋 ADJ cana-5016 140 6 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 141 1 βˆ’ βˆ’ NOUN cana-5016 141 2 ( ( PUNCT cana-5016 141 3 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 141 4 ) ) PUNCT cana-5016 141 5 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 142 1 + + CCONJ cana-5016 142 2 π›₯ π›₯ NOUN cana-5016 142 3 = = PUNCT cana-5016 142 4 βˆ’3 βˆ’3 NOUN cana-5016 142 5 2π‘Ž2 2π‘Ž2 NUM cana-5016 142 6 π‘’πœˆ π‘’πœˆ PROPN cana-5016 142 7 + + SYM cana-5016 142 8 8πœ‹πœŒπ‘šπ‘’ 8πœ‹πœŒπ‘šπ‘’ NUM cana-5016 142 9 ( ( PUNCT cana-5016 142 10 32 32 NUM cana-5016 142 11 ) ) PUNCT cana-5016 142 12 𝑛𝑋 𝑛𝑋 PROPN cana-5016 143 1 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 144 1 βˆ’ βˆ’ PROPN cana-5016 144 2 𝑛(π‘›βˆ’1 𝑛(π‘›βˆ’1 NOUN cana-5016 144 3 ) ) PUNCT cana-5016 144 4 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 145 1 + + CCONJ cana-5016 145 2 𝑛𝑋′ 𝑛𝑋′ PROPN cana-5016 145 3 4π‘Ÿ 4π‘Ÿ PROPN cana-5016 145 4 βˆ’ βˆ’ PROPN cana-5016 145 5 ( ( PUNCT cana-5016 145 6 π‘›βˆ’1)(π‘›βˆ’2 π‘›βˆ’1)(π‘›βˆ’2 NOUN cana-5016 145 7 ) ) PUNCT cana-5016 145 8 4π‘Ÿ2 4π‘Ÿ2 NOUN cana-5016 146 1 βˆ’ βˆ’ NOUN cana-5016 147 1 π›₯ π›₯ NOUN cana-5016 147 2 = = NOUN cana-5016 147 3 3 3 NUM cana-5016 147 4 2π‘Ž2 2π‘Ž2 NUM cana-5016 147 5 π‘’πœˆ π‘’πœˆ NOUN cana-5016 147 6 βˆ’ βˆ’ PROPN cana-5016 147 7 8πœ‹π‘ƒπ‘Ÿπ‘’ 8πœ‹π‘ƒπ‘Ÿπ‘’ NUM cana-5016 147 8 . . PUNCT cana-5016 148 1 ( ( PUNCT cana-5016 148 2 33 33 NUM cana-5016 148 3 ) ) PUNCT cana-5016 148 4 therefore therefore ADV cana-5016 148 5 , , PUNCT cana-5016 148 6 the the DET cana-5016 148 7 line line NOUN cana-5016 148 8 element element NOUN cana-5016 148 9 ( ( PUNCT cana-5016 148 10 2 2 NUM cana-5016 148 11 ) ) PUNCT cana-5016 148 12 , , PUNCT cana-5016 148 13 in in ADP cana-5016 148 14 terms term NOUN cana-5016 148 15 of of ADP cana-5016 148 16 π‘’πœˆ π‘’πœˆ NOUN cana-5016 148 17 = = SYM cana-5016 148 18 𝐢2 𝐢2 PROPN cana-5016 148 19 2π‘Ÿ2 2π‘Ÿ2 NUM cana-5016 148 20 , , PUNCT cana-5016 148 21 πœ“ πœ“ X cana-5016 148 22 = = X cana-5016 148 23 𝐢3 𝐢3 PROPN cana-5016 148 24 2π‘’βˆ’πœ†/2 2π‘’βˆ’πœ†/2 NUM cana-5016 148 25 and and CCONJ cana-5016 148 26 𝑋 𝑋 PROPN cana-5016 148 27 = = PUNCT cana-5016 148 28 πœ“2 πœ“2 PROPN cana-5016 148 29 𝐢3 𝐢3 NOUN cana-5016 148 30 2 2 NUM cana-5016 148 31 now now ADV cana-5016 148 32 becomes become VERB cana-5016 148 33 𝑑𝑠2 𝑑𝑠2 NOUN cana-5016 148 34 = = SYM cana-5016 148 35 𝐢2 𝐢2 X cana-5016 148 36 2π‘Ÿ2𝑑𝑑2 2π‘Ÿ2𝑑𝑑2 NUM cana-5016 148 37 βˆ’ βˆ’ PROPN cana-5016 148 38 ( ( PUNCT cana-5016 148 39 1 1 NUM cana-5016 148 40 𝑋 𝑋 NOUN cana-5016 148 41 ) ) PUNCT cana-5016 148 42 π‘‘π‘Ÿ2 π‘‘π‘Ÿ2 VERB cana-5016 148 43 βˆ’ βˆ’ NOUN cana-5016 148 44 π‘Ÿ2𝑑𝛺2 π‘Ÿ2𝑑𝛺2 NUM cana-5016 148 45 . . PUNCT cana-5016 149 1 ( ( PUNCT cana-5016 149 2 34 34 NUM cana-5016 149 3 ) ) PUNCT cana-5016 149 4 4 4 NUM cana-5016 149 5 . . PUNCT cana-5016 149 6 conclusions conclusion NOUN cana-5016 149 7 in in ADP cana-5016 149 8 this this DET cana-5016 149 9 paper paper NOUN cana-5016 150 1 , , PUNCT cana-5016 150 2 we we PRON cana-5016 150 3 have have AUX cana-5016 150 4 presented present VERB cana-5016 150 5 the the DET cana-5016 150 6 field field NOUN cana-5016 150 7 equations equation NOUN cana-5016 150 8 for for ADP cana-5016 150 9 anisotropic anisotropic NOUN cana-5016 150 10 charged charge VERB cana-5016 150 11 spheres sphere NOUN cana-5016 150 12 in in ADP cana-5016 150 13 higher high ADJ cana-5016 150 14 dimensional dimensional PROPN cana-5016 150 15 rosen rosen PROPN cana-5016 150 16 ’s ’s PART cana-5016 150 17 bimetric bimetric ADJ cana-5016 150 18 theory theory NOUN cana-5016 150 19 of of ADP cana-5016 150 20 relativity relativity NOUN cana-5016 150 21 . . PUNCT cana-5016 151 1 to to PART cana-5016 151 2 get get VERB cana-5016 151 3 a a DET cana-5016 151 4 determinate determinate ADJ cana-5016 151 5 solution solution NOUN cana-5016 151 6 of of ADP cana-5016 151 7 the the DET cana-5016 151 8 field field NOUN cana-5016 151 9 equations equation NOUN cana-5016 151 10 , , PUNCT cana-5016 151 11 we we PRON cana-5016 151 12 have have AUX cana-5016 151 13 assumed assume VERB cana-5016 151 14 that that SCONJ cana-5016 151 15 the the DET cana-5016 151 16 space space NOUN cana-5016 151 17 - - PUNCT cana-5016 151 18 time time NOUN cana-5016 151 19 admits admit VERB cana-5016 151 20 one one NUM cana-5016 151 21 parameter parameter NOUN cana-5016 151 22 group group NOUN cana-5016 151 23 of of ADP cana-5016 151 24 conformal conformal ADJ cana-5016 151 25 motion motion NOUN cana-5016 151 26 . . PUNCT cana-5016 152 1 it it PRON cana-5016 152 2 is be AUX cana-5016 152 3 observed observe VERB cana-5016 152 4 that that SCONJ cana-5016 152 5 the the DET cana-5016 152 6 solutions solution NOUN cana-5016 152 7 obtained obtain VERB cana-5016 152 8 in in ADP cana-5016 152 9 bimetric bimetric ADJ cana-5016 152 10 relativity relativity NOUN cana-5016 152 11 in in ADP cana-5016 152 12 higher high ADJ cana-5016 152 13 dimensions dimension NOUN cana-5016 152 14 will will AUX cana-5016 152 15 reduce reduce VERB cana-5016 152 16 to to ADP cana-5016 152 17 the the DET cana-5016 152 18 corresponding correspond VERB cana-5016 152 19 solutions solution NOUN cana-5016 152 20 of of ADP cana-5016 152 21 einstein einstein PROPN cana-5016 152 22 ’s ’s PART cana-5016 152 23 field field NOUN cana-5016 152 24 equations equation NOUN cana-5016 152 25 obtained obtain VERB cana-5016 152 26 by by ADP cana-5016 152 27 herrera herrera PROPN cana-5016 152 28 et et PROPN cana-5016 152 29 al al PROPN cana-5016 152 30 . . PUNCT cana-5016 153 1 [ [ X cana-5016 153 2 21 21 NUM cana-5016 153 3 ] ] PUNCT cana-5016 153 4 of of ADP cana-5016 153 5 a a DET cana-5016 153 6 physical physical ADJ cana-5016 153 7 system system NOUN cana-5016 153 8 , , PUNCT cana-5016 153 9 which which PRON cana-5016 153 10 is be AUX cana-5016 153 11 very very ADV cana-5016 153 12 small small ADJ cana-5016 153 13 compared compare VERB cana-5016 153 14 to to ADP cana-5016 153 15 the the DET cana-5016 153 16 size size NOUN cana-5016 153 17 of of ADP cana-5016 153 18 the the DET cana-5016 153 19 universe universe NOUN cana-5016 153 20 , , PUNCT cana-5016 153 21 when when SCONJ cana-5016 153 22 the the DET cana-5016 153 23 term term NOUN cana-5016 153 24 3 3 NUM cana-5016 153 25 2π‘Ž2 2π‘Ž2 NUM cana-5016 153 26 π‘’βˆ’πœˆ π‘’βˆ’πœˆ NOUN cana-5016 153 27 that that PRON cana-5016 153 28 appears appear VERB cana-5016 153 29 in in ADP cana-5016 153 30 the the DET cana-5016 153 31 field field NOUN cana-5016 153 32 equations equation NOUN cana-5016 153 33 of of ADP cana-5016 153 34 bimetric bimetric ADJ cana-5016 153 35 relativity relativity NOUN cana-5016 153 36 is be AUX cana-5016 153 37 negligible negligible ADJ cana-5016 153 38 . . PUNCT cana-5016 154 1 communications communication NOUN cana-5016 154 2 on on ADP cana-5016 154 3 applied apply VERB cana-5016 154 4 nonlinear nonlinear ADJ cana-5016 154 5 analysis analysis NOUN cana-5016 154 6 issn issn NOUN cana-5016 154 7 : : PUNCT cana-5016 154 8 1074 1074 NUM cana-5016 154 9 - - PUNCT cana-5016 154 10 133x 133x NUM cana-5016 154 11 vol vol NOUN cana-5016 154 12 31 31 NUM cana-5016 154 13 no no NOUN cana-5016 154 14 . . PUNCT cana-5016 155 1 8s 8s PROPN cana-5016 155 2 ( ( PUNCT cana-5016 155 3 2024 2024 NUM cana-5016 155 4 ) ) PUNCT cana-5016 155 5 910 910 NUM cana-5016 155 6 https://internationalpubls.com https://internationalpubls.com X cana-5016 155 7 references reference NOUN cana-5016 155 8 [ [ X cana-5016 155 9 1 1 NUM cana-5016 155 10 ] ] X cana-5016 155 11 rosen rosen PROPN cana-5016 155 12 , , PUNCT cana-5016 155 13 n. n. NOUN cana-5016 155 14 : : PUNCT cana-5016 155 15 lett lett PROPN cana-5016 155 16 . . PUNCT cana-5016 156 1 nuovo nuovo PROPN cana-5016 156 2 cim cim PROPN cana-5016 156 3 . . PROPN cana-5016 157 1 25 25 NUM cana-5016 157 2 , , PUNCT cana-5016 157 3 266 266 NUM cana-5016 157 4 ( ( PUNCT cana-5016 157 5 1979 1979 NUM cana-5016 157 6 ) ) PUNCT cana-5016 158 1 [ [ X cana-5016 158 2 2 2 NUM cana-5016 158 3 ] ] X cana-5016 158 4 rosen rosen PROPN cana-5016 158 5 , , PUNCT cana-5016 158 6 n. n. PROPN cana-5016 158 7 : : PUNCT cana-5016 158 8 found find VERB cana-5016 158 9 . . PUNCT cana-5016 159 1 phys phy NOUN cana-5016 159 2 . . PUNCT cana-5016 160 1 10 10 NUM cana-5016 160 2 , , PUNCT cana-5016 160 3 673 673 NUM cana-5016 160 4 ( ( PUNCT cana-5016 160 5 1980a 1980a NUM cana-5016 160 6 ) ) PUNCT cana-5016 161 1 [ [ X cana-5016 161 2 3 3 NUM cana-5016 161 3 ] ] X cana-5016 161 4 rosen rosen PROPN cana-5016 161 5 , , PUNCT cana-5016 161 6 n. n. NOUN cana-5016 161 7 : : PUNCT cana-5016 161 8 gen gen PROPN cana-5016 161 9 . . PROPN cana-5016 161 10 rel rel PROPN cana-5016 161 11 . . PUNCT cana-5016 162 1 grav grav PROPN cana-5016 162 2 . . PROPN cana-5016 163 1 12 12 NUM cana-5016 163 2 , , PUNCT cana-5016 163 3 493 493 NUM cana-5016 163 4 ( ( PUNCT cana-5016 163 5 1980b 1980b NUM cana-5016 163 6 ) ) PUNCT cana-5016 164 1 [ [ X cana-5016 164 2 4 4 NUM cana-5016 164 3 ] ] X cana-5016 164 4 rosen rosen PROPN cana-5016 164 5 , , PUNCT cana-5016 164 6 n. n. PROPN cana-5016 164 7 : : PUNCT cana-5016 164 8 ann ann PROPN cana-5016 164 9 . . PUNCT cana-5016 164 10 phys phy NOUN cana-5016 164 11 . . PUNCT cana-5016 165 1 84 84 NUM cana-5016 165 2 , , PUNCT cana-5016 165 3 455 455 NUM cana-5016 165 4 ( ( PUNCT cana-5016 165 5 1974 1974 NUM cana-5016 165 6 ) ) PUNCT cana-5016 166 1 [ [ X cana-5016 166 2 5 5 NUM cana-5016 166 3 ] ] X cana-5016 166 4 rosen rosen PROPN cana-5016 166 5 , , PUNCT cana-5016 166 6 n. n. NOUN cana-5016 166 7 : : PUNCT cana-5016 166 8 astrophys astrophy NOUN cana-5016 166 9 . . PUNCT cana-5016 167 1 j. j. PROPN cana-5016 167 2 221 221 NUM cana-5016 167 3 , , PUNCT cana-5016 167 4 284 284 NUM cana-5016 167 5 ( ( PUNCT cana-5016 167 6 1978b 1978b NUM cana-5016 167 7 ) ) PUNCT cana-5016 168 1 [ [ X cana-5016 168 2 6 6 NUM cana-5016 168 3 ] ] X cana-5016 168 4 rosen rosen PROPN cana-5016 168 5 , , PUNCT cana-5016 168 6 n. n. NOUN cana-5016 168 7 : : PUNCT cana-5016 168 8 gen gen PROPN cana-5016 168 9 . . PROPN cana-5016 168 10 rel rel PROPN cana-5016 168 11 . . PUNCT cana-5016 168 12 grav grav PROPN cana-5016 168 13 . . PUNCT cana-5016 169 1 9 9 NUM cana-5016 169 2 , , PUNCT cana-5016 169 3 339 339 NUM cana-5016 169 4 ( ( PUNCT cana-5016 169 5 1978a 1978a NUM cana-5016 169 6 ) ) PUNCT cana-5016 170 1 [ [ X cana-5016 170 2 7 7 X cana-5016 170 3 ] ] X cana-5016 170 4 kaluza kaluza PROPN cana-5016 170 5 , , PUNCT cana-5016 170 6 t. t. PROPN cana-5016 170 7 sitzungsber sitzungsber NOUN cana-5016 170 8 . . PUNCT cana-5016 171 1 preuss preuss ADJ cana-5016 171 2 . . PUNCT cana-5016 171 3 akad akad PROPN cana-5016 171 4 . . PUNCT cana-5016 172 1 wiss wiss PROPN cana-5016 172 2 . . PUNCT cana-5016 173 1 berlin berlin PROPN cana-5016 173 2 ( ( PUNCT cana-5016 173 3 math math NOUN cana-5016 173 4 . . PUNCT cana-5016 174 1 phys phy NOUN cana-5016 174 2 . . PUNCT cana-5016 174 3 ) ) PUNCT cana-5016 174 4 , , PUNCT cana-5016 174 5 1 1 NUM cana-5016 174 6 , , PUNCT cana-5016 174 7 966 966 NUM cana-5016 174 8 - - SYM cana-5016 174 9 972 972 NUM cana-5016 174 10 ( ( PUNCT cana-5016 174 11 1921 1921 NUM cana-5016 174 12 ) ) PUNCT cana-5016 175 1 [ [ X cana-5016 175 2 8 8 NUM cana-5016 175 3 ] ] X cana-5016 175 4 klein klein PROPN cana-5016 175 5 , , PUNCT cana-5016 175 6 o. o. PROPN cana-5016 175 7 zeits zeit NOUN cana-5016 175 8 . . PUNCT cana-5016 176 1 phys phy NOUN cana-5016 176 2 . . PUNCT cana-5016 177 1 37 37 NUM cana-5016 177 2 , , PUNCT cana-5016 177 3 895 895 NUM cana-5016 177 4 - - SYM cana-5016 177 5 906 906 NUM cana-5016 177 6 ( ( PUNCT cana-5016 177 7 1926 1926 NUM cana-5016 177 8 ) ) PUNCT cana-5016 178 1 [ [ X cana-5016 178 2 9 9 NUM cana-5016 178 3 ] ] SYM cana-5016 178 4 de de X cana-5016 178 5 sabbatta sabbatta NOUN cana-5016 178 6 , , PUNCT cana-5016 178 7 v. v. ADV cana-5016 178 8 ; ; PUNCT cana-5016 178 9 schmutzer schmutzer NOUN cana-5016 178 10 , , PUNCT cana-5016 178 11 e. e. PROPN cana-5016 178 12 unified unify VERB cana-5016 178 13 field field NOUN cana-5016 178 14 theories theory NOUN cana-5016 178 15 of of ADP cana-5016 178 16 more more ADJ cana-5016 178 17 than than ADP cana-5016 178 18 four four NUM cana-5016 178 19 dimensions dimension NOUN cana-5016 178 20 including include VERB cana-5016 178 21 exact exact ADJ cana-5016 178 22 solutions solution NOUN cana-5016 178 23 ; ; PUNCT cana-5016 178 24 world world NOUN cana-5016 178 25 scientific scientific NOUN cana-5016 178 26 : : PUNCT cana-5016 178 27 singapore singapore PROPN cana-5016 178 28 ( ( PUNCT cana-5016 178 29 1983 1983 NUM cana-5016 178 30 ) ) PUNCT cana-5016 179 1 [ [ X cana-5016 179 2 10 10 NUM cana-5016 179 3 ] ] X cana-5016 179 4 lee lee PROPN cana-5016 179 5 , , PUNCT cana-5016 179 6 h. h. PROPN cana-5016 179 7 c. c. PROPN cana-5016 180 1 an an DET cana-5016 180 2 introduction introduction NOUN cana-5016 180 3 to to ADP cana-5016 180 4 kaluza kaluza PROPN cana-5016 180 5 - - PUNCT cana-5016 180 6 klein klein PROPN cana-5016 180 7 theories theory NOUN cana-5016 180 8 ; ; PUNCT cana-5016 180 9 world world NOUN cana-5016 180 10 scientific scientific NOUN cana-5016 180 11 : : PUNCT cana-5016 180 12 singapore singapore PROPN cana-5016 180 13 ( ( PUNCT cana-5016 180 14 1984 1984 NUM cana-5016 180 15 ) ) PUNCT cana-5016 181 1 [ [ X cana-5016 181 2 11 11 NUM cana-5016 181 3 ] ] PUNCT cana-5016 181 4 appelquist appelquist NOUN cana-5016 181 5 , , PUNCT cana-5016 181 6 t. t. PROPN cana-5016 181 7 ; ; PUNCT cana-5016 181 8 chodos chodo NOUN cana-5016 181 9 , , PUNCT cana-5016 181 10 a. a. NOUN cana-5016 181 11 ; ; PUNCT cana-5016 181 12 freund freund PROPN cana-5016 181 13 , , PUNCT cana-5016 182 1 p. p. NOUN cana-5016 182 2 g. g. PROPN cana-5016 182 3 o. o. PROPN cana-5016 182 4 modern modern ADJ cana-5016 182 5 kaluza kaluza PROPN cana-5016 182 6 - - PUNCT cana-5016 182 7 klein klein PROPN cana-5016 182 8 theories theories PROPN cana-5016 182 9 ; ; PUNCT cana-5016 182 10 addison addison PROPN cana-5016 182 11 - - PUNCT cana-5016 182 12 wesley wesley PROPN cana-5016 182 13 : : PUNCT cana-5016 182 14 boston boston PROPN cana-5016 182 15 , , PUNCT cana-5016 182 16 ma ma PROPN cana-5016 182 17 , , PUNCT cana-5016 182 18 usa usa PROPN cana-5016 182 19 ( ( PUNCT cana-5016 182 20 1987 1987 NUM cana-5016 182 21 ) ) PUNCT cana-5016 183 1 [ [ X cana-5016 183 2 12 12 NUM cana-5016 183 3 ] ] PUNCT cana-5016 183 4 collins collin NOUN cana-5016 183 5 , , PUNCT cana-5016 183 6 p. p. PROPN cana-5016 183 7 d. d. PROPN cana-5016 183 8 b. b. PROPN cana-5016 183 9 ; ; PUNCT cana-5016 183 10 martin martin PROPN cana-5016 183 11 , , PUNCT cana-5016 183 12 a. a. PROPN cana-5016 183 13 d. d. PROPN cana-5016 183 14 ; ; PUNCT cana-5016 183 15 squires squire NOUN cana-5016 183 16 , , PUNCT cana-5016 183 17 e. e. PROPN cana-5016 183 18 j. j. PROPN cana-5016 183 19 particle particle PROPN cana-5016 183 20 physics physics PROPN cana-5016 183 21 and and CCONJ cana-5016 183 22 cosmology cosmology NOUN cana-5016 183 23 ; ; PUNCT cana-5016 183 24 wiley wiley PROPN cana-5016 183 25 : : PUNCT cana-5016 183 26 new new PROPN cana-5016 183 27 york york PROPN cana-5016 183 28 , , PUNCT cana-5016 183 29 ny ny PROPN cana-5016 183 30 , , PUNCT cana-5016 183 31 usa usa PROPN cana-5016 183 32 ( ( PUNCT cana-5016 183 33 1989 1989 NUM cana-5016 183 34 ) ) PUNCT cana-5016 184 1 [ [ X cana-5016 184 2 13 13 NUM cana-5016 184 3 ] ] SYM cana-5016 184 4 overduin overduin PROPN cana-5016 184 5 , , PUNCT cana-5016 184 6 j. j. PROPN cana-5016 184 7 m. m. PROPN cana-5016 184 8 ; ; PUNCT cana-5016 184 9 wesson wesson PROPN cana-5016 184 10 , , PUNCT cana-5016 184 11 p. p. NOUN cana-5016 184 12 s. s. PROPN cana-5016 184 13 phys phys PROPN cana-5016 184 14 . . PUNCT cana-5016 184 15 rep rep PROPN cana-5016 184 16 . . PROPN cana-5016 184 17 283 283 NUM cana-5016 184 18 , , PUNCT cana-5016 184 19 303 303 NUM cana-5016 184 20 - - SYM cana-5016 184 21 378 378 NUM cana-5016 184 22 ( ( PUNCT cana-5016 184 23 1997 1997 NUM cana-5016 184 24 ) ) PUNCT cana-5016 185 1 [ [ X cana-5016 185 2 14 14 NUM cana-5016 185 3 ] ] PUNCT cana-5016 185 4 mohanty mohanty PROPN cana-5016 185 5 , , PUNCT cana-5016 185 6 g. g. PROPN cana-5016 185 7 ; ; PUNCT cana-5016 185 8 mahanta mahanta PROPN cana-5016 185 9 , , PUNCT cana-5016 185 10 k. k. PROPN cana-5016 185 11 l. l. PROPN cana-5016 185 12 turk turk PROPN cana-5016 185 13 . . PUNCT cana-5016 186 1 j. j. PROPN cana-5016 186 2 phys phys PROPN cana-5016 186 3 . . PUNCT cana-5016 187 1 31 31 NUM cana-5016 187 2 , , PUNCT cana-5016 187 3 299 299 NUM cana-5016 187 4 - - SYM cana-5016 187 5 306 306 NUM cana-5016 187 6 ( ( PUNCT cana-5016 187 7 2007 2007 NUM cana-5016 187 8 ) ) PUNCT cana-5016 188 1 [ [ X cana-5016 188 2 15 15 NUM cana-5016 188 3 ] ] PUNCT cana-5016 188 4 mohanty mohanty NOUN cana-5016 188 5 , , PUNCT cana-5016 188 6 g. g. PROPN cana-5016 188 7 ; ; PUNCT cana-5016 188 8 mahanta mahanta PROPN cana-5016 188 9 , , PUNCT cana-5016 188 10 k. k. PROPN cana-5016 188 11 l. l. PROPN cana-5016 188 12 turk turk PROPN cana-5016 188 13 . . PUNCT cana-5016 189 1 j. j. PROPN cana-5016 189 2 phys phys PROPN cana-5016 189 3 . . PUNCT cana-5016 189 4 , , PUNCT cana-5016 189 5 32 32 NUM cana-5016 189 6 , , PUNCT cana-5016 189 7 299 299 NUM cana-5016 189 8 - - SYM cana-5016 189 9 303 303 NUM cana-5016 189 10 ( ( PUNCT cana-5016 189 11 2008 2008 NUM cana-5016 189 12 ) ) PUNCT cana-5016 190 1 [ [ X cana-5016 190 2 16 16 NUM cana-5016 190 3 ] ] PUNCT cana-5016 190 4 mohanty mohanty PROPN cana-5016 190 5 , , PUNCT cana-5016 190 6 g. g. PROPN cana-5016 190 7 ; ; PUNCT cana-5016 190 8 samanta samanta PROPN cana-5016 190 9 , , PUNCT cana-5016 190 10 g. g. PROPN cana-5016 190 11 c. c. PROPN cana-5016 190 12 turk turk PROPN cana-5016 190 13 . . PUNCT cana-5016 191 1 j. j. PROPN cana-5016 191 2 phys phys PROPN cana-5016 191 3 . . PUNCT cana-5016 192 1 32 32 NUM cana-5016 192 2 , , PUNCT cana-5016 192 3 251 251 NUM cana-5016 192 4 - - SYM cana-5016 192 5 260 260 NUM cana-5016 192 6 ( ( PUNCT cana-5016 192 7 2008 2008 NUM cana-5016 192 8 ) ) PUNCT cana-5016 193 1 [ [ X cana-5016 193 2 17 17 NUM cana-5016 193 3 ] ] X cana-5016 193 4 karade karade NOUN cana-5016 193 5 , , PUNCT cana-5016 193 6 t. t. NOUN cana-5016 193 7 m. m. NOUN cana-5016 193 8 ; ; PUNCT cana-5016 193 9 g. g. PROPN cana-5016 193 10 s. s. PROPN cana-5016 193 11 khadekar khadekar PROPN cana-5016 193 12 : : PUNCT cana-5016 193 13 czechoslovak czechoslovak PROPN cana-5016 193 14 j. j. PROPN cana-5016 193 15 of of ADP cana-5016 193 16 physics physics PROPN cana-5016 193 17 , , PUNCT cana-5016 193 18 39 39 NUM cana-5016 193 19 , , PUNCT cana-5016 193 20 9 9 NUM cana-5016 193 21 , , PUNCT cana-5016 193 22 962 962 NUM cana-5016 193 23 - - SYM cana-5016 193 24 967 967 NUM cana-5016 193 25 ( ( PUNCT cana-5016 193 26 1989 1989 NUM cana-5016 193 27 ) ) PUNCT cana-5016 194 1 [ [ X cana-5016 194 2 18 18 NUM cana-5016 194 3 ] ] X cana-5016 194 4 reddy reddy PROPN cana-5016 194 5 d.r.k d.r.k PROPN cana-5016 194 6 . . PUNCT cana-5016 194 7 , , PUNCT cana-5016 194 8 rao rao PROPN cana-5016 194 9 venkateswara venkateswara PROPN cana-5016 194 10 : : PUNCT cana-5016 194 11 astrophys astrophy NOUN cana-5016 194 12 . . PUNCT cana-5016 195 1 space space PROPN cana-5016 195 2 sci sci PROPN cana-5016 195 3 . . PROPN cana-5016 195 4 , , PUNCT cana-5016 195 5 271 271 NUM cana-5016 195 6 , , PUNCT cana-5016 195 7 2 2 NUM cana-5016 195 8 , , PUNCT cana-5016 195 9 165 165 NUM cana-5016 195 10 - - SYM cana-5016 195 11 169 169 NUM cana-5016 195 12 ( ( PUNCT cana-5016 195 13 2000 2000 NUM cana-5016 195 14 ) ) PUNCT cana-5016 196 1 [ [ X cana-5016 196 2 19 19 NUM cana-5016 196 3 ] ] PUNCT cana-5016 196 4 katore katore PROPN cana-5016 196 5 s. s. PROPN cana-5016 196 6 d. d. PROPN cana-5016 196 7 , , PUNCT cana-5016 196 8 adhav adhav PROPN cana-5016 196 9 k.s k.s PROPN cana-5016 196 10 . . PROPN cana-5016 196 11 , , PUNCT cana-5016 196 12 thakare thakare NOUN cana-5016 196 13 s.v s.v PROPN cana-5016 196 14 . . PROPN cana-5016 196 15 : : PUNCT cana-5016 197 1 astrophys astrophy NOUN cana-5016 197 2 . . PUNCT cana-5016 198 1 space space PROPN cana-5016 198 2 sci sci PROPN cana-5016 198 3 . . PROPN cana-5016 198 4 , , PUNCT cana-5016 198 5 299 299 NUM cana-5016 198 6 , , PUNCT cana-5016 198 7 3 3 NUM cana-5016 198 8 , , PUNCT cana-5016 198 9 233 233 NUM cana-5016 198 10 ( ( PUNCT cana-5016 198 11 2005 2005 NUM cana-5016 198 12 ) ) PUNCT cana-5016 199 1 [ [ X cana-5016 199 2 20 20 NUM cana-5016 199 3 ] ] X cana-5016 199 4 khadekar khadekar PROPN cana-5016 199 5 g. g. PROPN cana-5016 199 6 s. s. PROPN cana-5016 199 7 , , PUNCT cana-5016 199 8 tade tade PROPN cana-5016 199 9 s. s. PROPN cana-5016 199 10 d. d. PROPN cana-5016 199 11 : : PUNCT cana-5016 199 12 astrophys astrophy NOUN cana-5016 199 13 . . PUNCT cana-5016 200 1 space space PROPN cana-5016 200 2 sci sci PROPN cana-5016 200 3 . . PROPN cana-5016 200 4 , , PUNCT cana-5016 200 5 310 310 NUM cana-5016 200 6 , , PUNCT cana-5016 200 7 1 1 NUM cana-5016 200 8 , , PUNCT cana-5016 200 9 47 47 NUM cana-5016 200 10 - - SYM cana-5016 200 11 51 51 NUM cana-5016 200 12 ( ( PUNCT cana-5016 200 13 2007 2007 NUM cana-5016 200 14 ) ) PUNCT cana-5016 201 1 [ [ X cana-5016 201 2 21 21 NUM cana-5016 201 3 ] ] X cana-5016 201 4 herrera herrera NOUN cana-5016 201 5 , , PUNCT cana-5016 201 6 l. l. PROPN cana-5016 201 7 and and CCONJ cana-5016 201 8 ponce ponce PROPN cana-5016 201 9 de de PROPN cana-5016 201 10 leon leon PROPN cana-5016 201 11 , , PUNCT cana-5016 201 12 j. j. PROPN cana-5016 201 13 ( ( PUNCT cana-5016 201 14 1985 1985 NUM cana-5016 201 15 ) ) PUNCT cana-5016 201 16 j. j. PROPN cana-5016 201 17 math math PROPN cana-5016 201 18 . . PUNCT cana-5016 202 1 phys phy NOUN cana-5016 202 2 . . PUNCT cana-5016 203 1 26 26 NUM cana-5016 203 2 , , PUNCT cana-5016 203 3 2018 2018 NUM cana-5016 203 4 . . PUNCT cana-5016 204 1 [ [ X cana-5016 204 2 22 22 NUM cana-5016 204 3 ] ] X cana-5016 204 4 bowars bowar NOUN cana-5016 204 5 , , PUNCT cana-5016 204 6 r. r. PROPN cana-5016 204 7 and and CCONJ cana-5016 204 8 liang liang PROPN cana-5016 204 9 , , PUNCT cana-5016 204 10 e. e. PROPN cana-5016 204 11 : : PUNCT cana-5016 204 12 astrophys astrophys PROPN cana-5016 204 13 . . PUNCT cana-5016 205 1 j. j. PROPN cana-5016 205 2 188 188 NUM cana-5016 205 3 , , PUNCT cana-5016 205 4 657 657 NUM cana-5016 205 5 ( ( PUNCT cana-5016 205 6 1974 1974 NUM cana-5016 205 7 ) ) PUNCT cana-5016 206 1 [ [ X cana-5016 206 2 23 23 NUM cana-5016 206 3 ] ] X cana-5016 206 4 sah sah PROPN cana-5016 206 5 , , PUNCT cana-5016 206 6 a. a. NOUN cana-5016 206 7 ; ; PUNCT cana-5016 206 8 prakash prakash PROPN cana-5016 206 9 chandra chandra PROPN cana-5016 206 10 : : PUNCT cana-5016 206 11 international international ADJ cana-5016 206 12 journal journal NOUN cana-5016 206 13 of of ADP cana-5016 206 14 astronomy astronomy NOUN cana-5016 206 15 and and CCONJ cana-5016 206 16 astrophysics astrophysic NOUN cana-5016 206 17 , , PUNCT cana-5016 206 18 17 17 NUM cana-5016 206 19 , , PUNCT cana-5016 206 20 4 4 NUM cana-5016 206 21 , , PUNCT cana-5016 206 22 494 494 NUM cana-5016 206 23 - - SYM cana-5016 206 24 511 511 NUM cana-5016 206 25 ( ( PUNCT cana-5016 206 26 2016 2016 NUM cana-5016 206 27 ) ) PUNCT cana-5016 207 1 [ [ X cana-5016 207 2 24 24 NUM cana-5016 207 3 ] ] X cana-5016 207 4 hasmani hasmani PROPN cana-5016 207 5 , , PUNCT cana-5016 207 6 a.h a.h PROPN cana-5016 207 7 . . PROPN cana-5016 207 8 , , PUNCT cana-5016 207 9 pandya pandya PROPN cana-5016 207 10 , , PUNCT cana-5016 207 11 d.n d.n PROPN cana-5016 207 12 . . PROPN cana-5016 207 13 : : PUNCT cana-5016 207 14 journal journal NOUN cana-5016 207 15 of of ADP cana-5016 207 16 dynamical dynamical ADJ cana-5016 207 17 system system NOUN cana-5016 207 18 and and CCONJ cana-5016 207 19 geometric geometric ADJ cana-5016 207 20 theories theory NOUN cana-5016 207 21 , , PUNCT cana-5016 207 22 17(1 17(1 NUM cana-5016 207 23 ) ) PUNCT cana-5016 207 24 , , PUNCT cana-5016 207 25 1321 1321 NUM cana-5016 207 26 ( ( PUNCT cana-5016 207 27 2019 2019 NUM cana-5016 207 28 ) ) PUNCT cana-5016 208 1 [ [ X cana-5016 208 2 25 25 NUM cana-5016 208 3 ] ] X cana-5016 208 4 mukesh mukesh PROPN cana-5016 208 5 kumar kumar PROPN cana-5016 208 6 madhukar madhukar PROPN cana-5016 208 7 : : PUNCT cana-5016 208 8 journal journal NOUN cana-5016 208 9 of of ADP cana-5016 208 10 advances advance NOUN cana-5016 208 11 and and CCONJ cana-5016 208 12 scholarly scholarly ADJ cana-5016 208 13 researches research NOUN cana-5016 208 14 in in ADP cana-5016 208 15 allied allied ADJ cana-5016 208 16 education education NOUN cana-5016 208 17 , , PUNCT cana-5016 208 18 17 17 NUM cana-5016 208 19 , , PUNCT cana-5016 208 20 1 1 NUM cana-5016 208 21 , , PUNCT cana-5016 208 22 606 606 NUM cana-5016 208 23 608 608 NUM cana-5016 208 24 ( ( PUNCT cana-5016 208 25 3 3 NUM cana-5016 208 26 ) ) PUNCT cana-5016 208 27 ( ( PUNCT cana-5016 208 28 2020 2020 NUM cana-5016 208 29 ) ) PUNCT cana-5016 209 1 [ [ X cana-5016 209 2 26 26 NUM cana-5016 209 3 ] ] X cana-5016 209 4 francesco francesco PROPN cana-5016 209 5 bajardi bajardi PROPN cana-5016 209 6 , , PUNCT cana-5016 209 7 konstantinos konstantinos PROPN cana-5016 209 8 f. f. PROPN cana-5016 209 9 , , PUNCT cana-5016 209 10 dialektopoulos dialektopoulos PROPN cana-5016 209 11 , , PUNCT cana-5016 209 12 capozziello capozziello PROPN cana-5016 209 13 , , PUNCT cana-5016 209 14 s. s. PROPN cana-5016 209 15 : : PUNCT cana-5016 209 16 symmetry symmetry NOUN cana-5016 209 17 , , PUNCT cana-5016 209 18 12 12 NUM cana-5016 209 19 ( ( PUNCT cana-5016 209 20 3 3 NUM cana-5016 209 21 ) ) PUNCT cana-5016 209 22 , , PUNCT cana-5016 209 23 372 372 NUM cana-5016 209 24 ( ( PUNCT cana-5016 209 25 2020 2020 NUM cana-5016 209 26 ) ) PUNCT cana-5016 210 1 [ [ X cana-5016 210 2 27 27 NUM cana-5016 210 3 ] ] PUNCT cana-5016 210 4 zahraa zahraa PROPN cana-5016 210 5 , , PUNCT cana-5016 210 6 a. a. PROPN cana-5016 210 7 ; ; PUNCT cana-5016 210 8 mardanb mardanb PROPN cana-5016 210 9 , , PUNCT cana-5016 210 10 s.a s.a PROPN cana-5016 210 11 . . PROPN cana-5016 210 12 : : PUNCT cana-5016 211 1 the the DET cana-5016 211 2 european european PROPN cana-5016 211 3 physical physical PROPN cana-5016 211 4 journal journal PROPN cana-5016 211 5 c c PROPN cana-5016 211 6 , , PUNCT cana-5016 211 7 83:231 83:231 NUM cana-5016 211 8 ( ( PUNCT cana-5016 211 9 2023 2023 NUM cana-5016 211 10 ) ) PUNCT