Depth to the minimal surface and radius of the entrance to the black hole

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-07-03 DOI:10.1016/j.geomphys.2024.105267

Seong-Hun Paeng

引用次数: 0

Abstract

An asymptotically flat manifold is the union of an almost flat region and a compact non flat region. If there exists a black hole, we will call the boundary of non flat region the entrance to the black hole. Also, we will call the distance from the entrance to the outermost minimal surface the depth. We use an integral norm of Ricci curvature to obtain positive lower bounds on the depth and the radius of the entrance. Also we obtain an upper bound of the number of ends from the integral norm of Ricci curvature.

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黑洞最小表面深度和入口半径

渐近平坦流形是一个几乎平坦区域和一个紧凑非平坦区域的结合。如果存在黑洞，我们将把非平坦区域的边界称为黑洞的边界。同时，我们把从入口到最外层极小曲面的距离称为（图 1）。我们使用里奇曲率的积分规范来获得入口深度和半径的正下限。此外，我们还可以从利玛窦曲率积分规范中得到端点数的上限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity