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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 isolated horizon ： ウィキペディア英語版 isolated horizon It was customary to represent black hole horizons via stationary solutions of field equations, i.e, solutions which admit a time-translational Killing vector field everywhere, not just in a small neighborhood of the black hole. While this simple idealization was natural as a starting point, it is overly restrictive. Physically, it should be sufficient to impose boundary conditions at the horizon which ensure only that the black hole itself is isolated. That is, it should suffice to demand only that the intrinsic geometry of the horizon be time independent, whereas the geometry outside may be dynamical and admit gravitational and other radiation. An advantage of isolated horizons over event horizons is that while one needs the entire spacetime history to locate an event horizon, isolated horizons are defined using local spacetime structures only. The laws of black hole mechanics, initially proved for event horizons, are generalized to isolated horizons. An isolated horizon $(\backslash Delta\backslash ,,())$ refers to the quasilocal definition〔Ivan Booth. ''Black hole boundaries''. Canadian Journal of Physics, 2005, 83(11): 1073-1099. (arXiv:gr-qc/0508107v2 )〕 of a black hole which is in equilibrium with its exterior,〔Abhay Ashtekar, Christopher Beetle, Olaf Dreyer, et al. ''Generic isolated horizons and their applications''. Physical Review Letters, 2000, 85(17): 3564-3567.(arXiv:gr-qc/0006006v2 )〕〔Abhay Ashtekar, Christopher Beetle, Jerzy Lewandowski. ''Geometry of generic isolated horizons''. Classical and Quantum Gravity, 2002, 19(6): 1195-1225. (arXiv:gr-qc/0111067v2 )〕〔Abhay Ashtekar, Stephen Fairhurst, Badri Krishnan. ''Isolated horizons: Hamiltonian evolution and the first law''. Physical Review D, 2000, 62(10): 104025. (gr-qc/0005083 )〕 and both the intrinsic and extrinsic structures of an isolated horizon (IH) are preserved by the ''null equivalence class'' $()$. The concept of IHs is developed based on the ideas of non-expanding horizons (NEHs) and weakly isolated horizons (WIHs): A NEH is a null surface whose ''intrinsic'' structure is preserved and constitutes the geometric prototype of WIHs and IHs, while a WIH is a NEH with a well-defined surface gravity and based on which the black-hole mechanics can be quasilocally generalized. ==Definition of IHs== A three-dimensional submanifold $\backslash Delta$ equipped with an equivalence class $()$ is defined as an IH if it respects the following conditions:〔〔〔 (i) $\backslash Delta$ is null and topologically $S^2\backslash times\backslash mathbb$; (ii) Along any null normal field $l$ tangent to $\backslash Delta$, the outgoing expansion rate $\backslash displaystyle\; \backslash theta\_:=\backslash hat^\backslash hat\_a\; l\_b$ vanishes; (iii) All field equations hold on $\backslash Delta$, and the stress–energy tensor $T\_$ on $\backslash Delta$ is such that $V^a:=-T^a\_b\; l^b$ is a future-directed causal vector ($V^a\; V\_a\backslash leq\; 0$) for any future-directed null normal $l^a$. (iv) The commutator $(\backslash mathcal\_a)=0$, where $\backslash mathcal\_a$ denotes the induced connection on the horizon. Note: Following the convention set up in refs.,〔〔〔 "hat" over the equality symbol $\backslash hat=$ means equality on the black-hole horizons (NEHs), and "hat" over quantities and operators ($\backslash hat\; h^$, $\backslash hat\backslash nabla$, etc) denotes those on the horizon or on a foliation leaf of the horizon (this makes no difference for IHs). 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「isolated horizon」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.