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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 Ozsváth–Schücking metric ： ウィキペディア英語版 Ozsváth–Schücking metric The Ozsváth–Schücking metric, or the Ozsváth–Schücking solution, is a vacuum solution of the Einstein field equations. The metric was published by István Ozsváth and Engelbert Schücking in 1962. It is noteworthy among vacuum solutions for being the first known solution that is stationary, globally defined, and singularity-free but nevertheless not isometric to the Minkowski metric. This stands in contradiction to a claimed strong Mach principle, which would forbid a vacuum solution from being anything but Minkowski without singularities, where the singularities are to be construed as mass as in the Schwarzschild metric. With coordinates $\backslash$, define the following tetrad: :$e\_=\backslash frac=\backslash frac\backslash right)\backslash partial\_0+\backslash left(1+(x^3)^2-x^3\backslash sqrt\backslash right)\backslash partial\_1+\backslash partial\_2\backslash right\; )$ :$e\_=\backslash frac\backslash right)\backslash partial\_0+\backslash left(1+(x^3)^2+x^3\backslash sqrt\backslash right)\backslash partial\_1+\backslash partial\_2\backslash right\; )$ :$e\_=\backslash partial\_3$ It is straightforward to verify that e(0) is timelike, e(1), e(2), e(3) are spacelike, that they are all orthogonal, and that there are no singularities. The corresponding proper time is :$^\; =\; -(dx^0)^2\; +4(x^3)(dx^0)(dx^2)-2(dx^1)(dx^2)-2(x^3)^2(dx^2)^2-(dx^3)^2.$ The Riemann tensor has only one algebraically independent, nonzero component :$R\_=-1,$ which shows that the spacetime is Ricci flat but not conformally flat. That is sufficient to conclude that it is a vacuum solution distinct from Minkowski spacetime. Under a suitable coordinate transformation, the metric can be rewritten as :$$ d\tau^2 = (- y^2) \cos (2u) + 2xy \sin(2u) ) du^2 - 2dudv - dx^2 - dy^2 and is therefore an example of a pp-wave spacetime. ==References== 〔 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「Ozsváth–Schücking metric」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.