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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 Kruskal–Szekeres coordinates ： ウィキペディア英語版 Kruskal–Szekeres coordinates In general relativity Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity. ==Definition== Kruskal–Szekeres coordinates are defined, from the Schwarzschild coordinates $(t,r,\backslash theta,\backslash phi)$, by replacing ''t'' and ''r'' by a new time coordinate ''T'' and a new spatial coordinate ''X'': :$T\; =\; \backslash left(\backslash frac\; -\; 1\backslash right)^e^\backslash sinh\backslash left(\backslash frac\backslash right)$ :$X\; =\; \backslash left(\backslash frac\; -\; 1\backslash right)^e^\backslash cosh\backslash left(\backslash frac\backslash right)$ for the exterior region $r>2GM$, and: :$T\; =\; \backslash left(1\; -\; \backslash frac\backslash right)^e^\backslash cosh\backslash left(\backslash frac\backslash right)$ :$X\; =\; \backslash left(1\; -\; \backslash frac\backslash right)^e^\backslash sinh\backslash left(\backslash frac\backslash right)$ for the interior region It follows that the Schwarzschild ''r'', in terms of Kruskal–Szekeres coordinates, is implicitly given by: :$T^2\; -\; X^2\; =\; \backslash left(1-\backslash frac\backslash right)e^$ or using the Lambert W function as: :$\backslash frac\; =\; 1\; +\; W\; \backslash left(\; \backslash frac\; \backslash right)$. In these new coordinates the metric of the Schwarzschild black hole manifold is given by :$ds^\; =\; \backslash frace^(-dT^2\; +\; dX^2)\; +\; r^2\; d\backslash Omega^2,$ written using the (− + + +) metric signature convention and where the angular component of the metric (the line element of the 2-sphere) is: :$d\backslash Omega^2\backslash \; \backslash stackrel\backslash \; d\backslash theta^2+\backslash sin^2\backslash theta\backslash ,d\backslash phi^2$ The location of the event horizon (''r'' = 2''GM'') in these coordinates is given by $T\; =\; \backslash plusmn\; X\backslash ,$. Note that the metric is perfectly well defined and non-singular at the event horizon. The curvature singularity is located at $T^2\; -\; X^2\; =\; 1$. 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「Kruskal–Szekeres coordinates」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.