论文标题

爱因斯坦方程的大d极限

The Large D Limit of Einstein's Equations

论文作者

Emparan, Roberto, Herzog, Christopher P.

论文摘要

我们回顾了达到爱因斯坦方程的较大维度限制的最新进展。我们的大多数分析本质上都是经典的,并且是存在黑洞地平线的问题,尽管我们简要讨论了包括量子重力效应的各种扩展。该评论由两个主要部分组成:第一次讨论黑洞的一般方面和在这个大维限制下的有效膜理论,第二个是对有趣的物理问题的一系列应用。第一部分包括对准模式的讨论,该模式自然地导致描述了描述近型几何形状的有效流体动力学方程的描述。这些有效的理论有两种主要方法 - 一种完全协变量的方法和一种部分衡量的方法 - 我们相互讨论。在第二部分中,我们将应用程序分为三个主要类别:Gregory-Laflamme不稳定性,黑洞碰撞和合并,以及反DE的保姆/共形场理论对应关系(ADS/CFT)。 ADS/CFT提出了引力理论与强烈相互作用的田间理论之间的等效性,从而使我们能够将应用范围扩展到流体动力学,凝结物理学和核物理学的问题。评论的最后一个简短的部分描述了进一步的有希望的方向,到目前为止,很少有研究文章。

We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions that include quantum gravitational effects. The review consists of two main parts: the first a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes which leads naturally into a description of effective hydrodynamic-like equations that describe the near horizon geometry. There are two main approaches to these effective theories -- a fully covariant approach and a partially gauge-fixed one -- which we discuss in relation to each other. In the second part we divide the applications up into three main categories: the Gregory-Laflamme instability, black hole collisions and mergers, and the anti-de Sitter/conformal field theory correspondence (AdS/CFT). AdS/CFT posits an equivalence between a gravitational theory and a strongly interacting field theory, allowing us to extend our spectrum of applications to problems in hydrodynamics, condensed matter physics, and nuclear physics. A final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles.

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