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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 Non-expanding horizon ： ウィキペディア英語版 Non-expanding horizon A non-expanding horizon (NEH) is an enclosed null surface whose intrinsic structure is preserved. An NEH is the geometric prototype of an isolated horizon which describes a black hole in equilibrium with its exterior from the quasilocal perspective. It is based on the concept and geometry of NEHs that the two quasilocal definitions of black holes, weakly isolated horizons and isolated horizons, are developed. == Definition of NEHs == A three-dimensional submanifold ∆ is defined as a ''generic'' (rotating and distorted) NEH if it respects the following conditions:〔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 )〕 (i) ∆ is null and topologically $S^2\backslash times\backslash mathbb$; (ii) Along any null normal field $l$ tangent to ∆, the outgoing expansion rate $\backslash displaystyle\; \backslash theta\_:=\backslash hat^\backslash hat\_a\; l\_b$ vanishes; (iii) All field equations hold on ∆, and the stress–energy tensor $T\_$ on ∆ 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 $l^a$. Condition (i) is fairly trivial and just states the general fact that from a 3+1 perspective〔Thomas W Baumgarte, Stuart L Shapiro. ''Numerical Relativity: Solving Einstein's Equations on the Computer''. Cambridge: Cambridge University Press, 2010. Chapter 2: The 3+1 decomposition of Einstein's equations, page 23.〕 an NEH ∆ is foliated by spacelike 2-spheres ∆'=S2, where S2 emphasizes that ∆' is topologically compact with genus zero ($g=0$). The signature of ∆ is (0,+,+) with a degenerate temporal coordinate, and the intrinsic geometry of a foliation leaf ∆'=S2 is nonevolutional. The property $\backslash theta\_=0$ in condition (ii) plays a pivotal role in defining NEHs and the rich implications encoded therein will be extensively discussed below. Condition (iii) makes one feel free to apply the Newman–Penrose (NP) formalism〔Jeremy Bransom Griffiths, Jiri Podolsky. ''Exact Space-Times in Einstein's General Relativity''. Cambridge: Cambridge University Press, 2009. Chapter 2.〕〔Valeri P Frolov, Igor D Novikov. ''Black Hole Physics: Basic Concepts and New Developments''. Berlin: Springer, 1998. Appendix E.〕 of Einstein-Maxwell field equations to the horizon and its near-horizon vicinity; furthermore, the very energy inequality is motivated from the dominant energy condition〔 and is a sufficient condition for deriving many boundary conditions of NEHs. ''Note'': In this article, 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 a foliation leaf of the horizon. Also, ∆ is the ''standard'' symbol for both an NEH and the directional derivative ∆$:=n^a\backslash nabla\_a$ in NP formalism, and we believe this won't cause an ambiguity. 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「Non-expanding 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.