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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 Belinski–Zakharov transform ： ウィキペディア英語版 Belinski–Zakharov transform The Belinski–Zakharov (inverse) transform is a nonlinear transformation that generates new exact solutions of the vacuum Einstein's field equation. It was developed by Vladimir Belinski and Vladimir Zakharov in 1978.〔V. Belinskii and V. Zakharov, Integration of the Einstein Equations by Means of the Inverse Scattering Problem Technique and Construction of Exact Soliton Solutions, Sov. Phys. JETP 48(6) (1978)〕 The Belinski–Zakharov transform is a generalization of the inverse scattering transform. The solutions produced by this transform are called gravitational solitons (gravisolitons). Despite the term 'soliton' being used to describe gravitational solitons, their behavior is very different from other (classical) solitons.〔V. Belinski and E. Verdaguer, Gravitational Solitons, Cambridge Monographs on Mathematical Physics (2001)〕 In particular, gravitational solitons do not preserve their amplitude and shape in time, and up to June 2012 their general interpretation remains unknown. What is known however, is that most black holes (and particularly the Schwarzschild metric and the Kerr metric) are special cases of gravitational solitons. == Introduction == The Belinski–Zakharov transform works for spacetime intervals of the form ::$ds^2\; =\; f\; (-d(x^0)^2\; +\; d(x^1)^2)\; +\; g\_\; \backslash ,\; dx^a\; \backslash ,\; dx^b$ where we use Einstein's summation convention for $a,b=2,3$. It is assumed that both the function $f$ and the matrix $g=g\_$ depend on the coordinates $x^0$ and $x^1$ only. Despite being a specific form of the spacetime interval that depends only on two variables, it includes a great number of interesting solutions a special cases, such as the Schwarzschild metric, the Kerr metric, Einstein–Rosen metric, and many others. In this case, Einstein's vacuum equation $R\_=0$ decomposes into two sets of equations for the matrix $g=g\_$ and the function $f$. Using light-cone coordinates $\backslash zeta\; =\; x^0\; +\; x^1,\backslash eta\; =\; x^0\; -\; x^1$, the first equation for the matrix $g$ is ::$(\backslash alpha\; g\_\; g^)\_\; +\; (\backslash alpha\; g\_\; g^)\_\; =\; 0$ where $\backslash alpha$ is the square root of the determinant of $g$, namely ::$\backslash det\; g=\backslash alpha^2$ The second set of equations is ::$(\backslash ln\; f)\_\; =\; \backslash frac\}\; +\; \backslash frac\; (g\_\; g^\; g\_\; g^)$ ::$(\backslash ln\; f)\_\; =\; \backslash frac\}\; +\; \backslash frac\; (g\_\; g^\; g\_\; g^)$ Taking the trace of the matrix equation for $g$ reveals that in fact $\backslash alpha$ satisfies the wave equation ::$\backslash alpha\_=0$ 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「Belinski–Zakharov transform」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.