id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
american_scientific_journal-1402	Wimaladharma, Sashinka; Silva, Nalin de	A Static Solution to Einstein’s Field Equations for a Spherical Distribution of Electrically Counterpoised Dust	2016	10	.pdf	application/pdf	3099	109	66	Substituting Δ𝑑𝑑0′ = Δ𝑑𝑑0 in (33), we obtain 𝜐𝜐0 𝜐𝜐0′ = �𝜃𝜃�𝑎𝑎𝑙𝑙�− 𝑚𝑚 𝑎𝑎+ 𝑚𝑚 𝑅𝑅0 � �𝜃𝜃�𝑎𝑎𝑙𝑙�� (34) Using the fact 𝜈𝜈0 𝜈𝜈𝑒𝑒 = 𝜐𝜐0 𝜐𝜐0′ 𝜐𝜐0′ 𝜐𝜐𝑒𝑒′ 𝜈𝜈𝑒𝑒′ 𝜈𝜈𝑒𝑒 and the equations (23), (26) and (34), we obtain 𝜈𝜈0 𝜈𝜈𝑒𝑒 = �𝜃𝜃�𝑎𝑎𝑙𝑙�− 𝑚𝑚 𝑎𝑎+ 𝑚𝑚 𝑅𝑅0 � �𝜃𝜃�𝑎𝑎𝑙𝑙�� �𝜃𝜃�𝑎𝑎𝑙𝑙�� �𝜃𝜃�𝑅𝑅𝑒𝑒𝑙𝑙 �� (35) Since the red shift z corresponds to the change of the wave length, we have 1 + 𝑧𝑧 = 𝜆𝜆0 𝜆𝜆𝑒𝑒 = 𝜃𝜃�𝑅𝑅𝑒𝑒𝑙𝑙 � �𝜃𝜃�𝑎𝑎𝑙𝑙�− 𝑚𝑚 𝑎𝑎+ 𝑚𝑚 𝑅𝑅0 � (36) Since the number of cycles of the pulse remain the same throughout its way, we obtain 𝜐𝜐0 𝜐𝜐0′ = Δ𝜏𝜏0′ Δ𝜏𝜏0 (32) Substitution (31) in (32) gives 𝜐𝜐0 𝜐𝜐0′ = �𝜃𝜃�𝑎𝑎𝑙𝑙�− 𝑚𝑚 𝑎𝑎+ 𝑚𝑚 𝑅𝑅0 � �𝜃𝜃�𝑎𝑎𝑙𝑙�� �Δ𝑑𝑑0 ′ Δ𝑑𝑑0 � (33)	cache/american_scientific_journal-1402.pdf	txt/american_scientific_journal-1402.txt