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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 Lemaître coordinates ： ウィキペディア英語版 Lemaître coordinates Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric – a spherically symmetric solution to the Einstein field equations in a vacuum – obtained by Monsignor Georges Lemaître in 1932.〔 English translation: See also:  … 〕 Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius. ==The Lemaître coordinates == The original Schwarzschild coordinate expression of the Schwarzschild metric, in natural units (), is given as :$ds^2=\backslash left(1-\backslash right)dt^2-$ to the new coordinates $\backslash ,$ :$$ \begin d\tau = dt + \sqrt}\frac)}dr~\\ d\rho = dt + \sqrt}}\frac)}dr~ \end (notice that the numerator and denominator are switched inside the square-roots), leads to the Lemaître coordinate expression of the metric, :$$ ds^ = d\tau^ - \frac d\rho^ - r^(d\theta^ +\sin^\theta d\phi^) where :$$ r=\left()^r_^ \;. The trajectories ''ρ'' constant are timelike geodesics with ''τ'' the proper time along these geodesics. They represent the motion of freely falling particles which start out with zero velocity at infinity. At any point their speed is just equal to the escape velocity from that point. In Lemaître coordinates there is no singularity at the gravitational radius, which instead corresponds to the point $\backslash frac(\backslash rho-\backslash tau)=r\_g$. However, there remains a genuine gravitational singularity at the center, where $\backslash rho-\backslash tau=0$, which cannot be removed by a coordinate change. The Lemaître coordinate system is synchronous, that is, the global time coordinate of the metric defines the proper time of co-moving observers. The radially falling bodies reach the gravitational radius and the centre within finite proper time. Along the trajectory of a radial light ray, :$$ dr=\left(\pm 1 - \sqrt\right)d\tau , therefore no signal can escape from inside the Schwarzschild radius, where always and the light rays emitted radially inwards and outwards both end up at the origin. 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「Lemaître 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.