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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Etherington's reciprocity theorem ： ウィキペディア英語版 Etherington's reciprocity theorem The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular diameter distance.〔I.M.H. Etherington, “LX. On the Definition of Distance in General Relativity”, Philosophical Magazine, Vol. 15, S. 7 (1933), pp. 761-773.〕 The equation is as follows: $d\_L=(1+z)^2\; d\_A$, where $d\_L$ is the luminosity distance and $d\_A$ the angular-diameter distance. == History and derivations == When Etherington introduced this equation in 1933, he mentioned that this equation was proposed by Tolman as a way to test a cosmological model. Ellis proposed a proof of this equation in the context of Riemannian geometry.〔G.F.R. Ellis, “Relativistic cosmology”, Proceedings of the 47th International School of Physics “Enrico Fermi”, edited by R.K. Sachs (Academic Press, New York and London), Vol. 15 (1971), pp. 104-182.〕〔G.F.R. Ellis, “On the Definition of Distance in General Relativity: I.M.H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933))”, General Relativity and Gravitation, Vol.39 (2007), pp. 1047–1052.〕 A quote from Ellis: "The core of the reciprocity theorem is the fact that many geometric properties are invariant when the roles of the source and observer in astronomical observations are transposed". This statement is fundamental in the derivation of the reciprocity theorem. The Etherington's reciprocity theorem was derived recently for a static universe; although this is more a pedagogical exercise.〔Y. Heymann. A Derivation of the Etherington’s Distance-Duality Equation. International Journal of Astrophysics and Space Science, Vol. 3, No. 4, 2015, pp. 65-69.()〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Etherington's reciprocity theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.