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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 Deriving the Schwarzschild solution ： ウィキペディア英語版 Deriving the Schwarzschild solution The Schwarzschild solution is one of the simplest and most useful solutions of the Einstein field equations (see general relativity). It describes spacetime in the vicinity of a non-rotating massive spherically-symmetric object. It is worthwhile deriving this metric in some detail; the following is a reasonably rigorous derivation that is not always seen in the textbooks. == Assumptions and notation == Working in a coordinate chart with coordinates $\backslash left(r,\; \backslash theta,\; \backslash phi,\; t\; \backslash right)$ labelled 1 to 4 respectively, we begin with the metric in its most general form (10 independent components, each of which is a smooth function of 4 variables). The solution is assumed to be spherically symmetric, static and vacuum. For the purposes of this article, these assumptions may be stated as follows (see the relevant links for precise definitions): # A spherically symmetric spacetime is one that is invariant under rotations and taking the mirror image. # A static spacetime is one in which all metric components are independent of the time coordinate $t$ (so that $\backslash tfrac\backslash partg\_=0$) and the geometry of the spacetime is unchanged under a time-reversal $t\; \backslash rightarrow\; -t$. # A vacuum solution is one that satisfies the equation $T\_=0$. From the Einstein field equations (with zero cosmological constant), this implies that $R\_=0$ since contracting $R\_-\backslash tfrac\; g\_=0$ yields $R\; =\; 0$. # Metric signature used here is (+,+,+,−). 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「Deriving the Schwarzschild solution」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.