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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 Boyer–Lindquist coordinates ： ウィキペディア英語版 Boyer–Lindquist coordinates In the mathematical description of general relativity, the Boyer–Lindquist coordinates are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole. The coordinate transformation from Boyer–Lindquist coordinates $r,\; \backslash theta$, $\backslash phi$ to cartesian coordinates x, y, z is given by ::$=\; \backslash sqrt\; \backslash sin\backslash theta\backslash cos\backslash phi$ ::$=\; \backslash sqrt\; \backslash sin\backslash theta\backslash sin\backslash phi$ ::$=\; r\; \backslash cos\backslash theta\; \backslash quad$ The line element for a black hole with mass $M$, angular momentum $J$, and charge $Q$ in Boyer–Lindquist coordinates and natural units ($G=c=1$) is ::$ds^2\; =\; -\backslash frac\backslash left(dt\; -\; a\; \backslash sin^2\backslash theta\; d\backslash phi\; \backslash right)^2\; +\backslash frac\backslash Big((r^2+a^2)d\backslash phi\; -\; a\; dt\backslash Big)^2\; +\; \backslash fracdr^2\; +\; \backslash Sigma\; d\backslash theta^2$ where ::$\backslash Delta\; =\; r^2\; -\; 2Mr\; +\; a^2\; +\; Q^2$ ::$\backslash Sigma\; =\; r^2\; +\; a^2\; \backslash cos^2\backslash theta$ ::$a\; =\; J/M$, the angular momentum per unit mass of the black hole Note that in natural units $M$, $a$, and $Q$ all have units of length. This line element describes the Kerr–Newman metric. The Hamiltonian for test particle motion in Kerr spacetime was separable in Boyer–Lindquist coordinates. Using Hamilton-Jacobi theory one can derive a fourth constant of the motion known as Carter's constant. ==References == *Boyer, R. H. and Lindquist, R. W. ''Maximal Analytic Extension of the Kerr Metric''. J. Math. Phys. 8, 265-281, 1967. *Shapiro, S. L. and Teukolsky, S. A. ''Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects''. New York: Wiley, p. 357, 1983. 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「Boyer–Lindquist 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.