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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 Riemannian Penrose inequality ： ウィキペディア英語版 Riemannian Penrose inequality In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The Riemannian Penrose inequality is an important special case. Specifically, if (''M'', ''g'') is an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and ADM mass ''m'', and ''A'' is the area of the outermost minimal surface (possibly with multiple connected components), then the Riemannian Penrose inequality asserts : $m\; \backslash geq\; \backslash sqrt\}.$ This is purely a geometrical fact, and it corresponds to the case of a complete three-dimensional, space-like, totally geodesic submanifold of a (3 + 1)-dimensional spacetime. Such a submanifold is often called a time-symmetric initial data set for a spacetime. The condition of (''M'', ''g'') having nonnegative scalar curvature is equivalent to the spacetime obeying the dominant energy condition. This inequality was first proved by Gerhard Huisken and Tom Ilmanen in 1997 in the case where ''A'' is the area of the largest component of the outermost minimal surface. Their proof relied on the machinery of weakly defined inverse mean curvature flow, which they developed. In 1999, Hubert Bray gave the first complete proof of the above inequality using a conformal flow of metrics. Both of the papers were published in 2001. == Physical motivation == The original physical argument that led Penrose to conjecture such an inequality invoked the Hawking area theorem and the Cosmic censorship hypothesis. 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「Riemannian Penrose inequality」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.