Recent progress in taking the large dimension limit of Einstein’s equations is reviewed. Most of the analysis is classical and concerns situations where there is a black hole horizon, although various extensions that include quantum gravitational effects are discussed. The review consists of two main parts: the first is a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second is a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes that leads naturally into a description of effective hydrodynamiclike 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 are discussed in relation to each other. In the second part the applications are divided up into three main categories: the Gregory-Laflamme instability, black hole collisions and mergers, and the anti–de Sitter/conformal field theory correspondence ($\mathrm{AdS}/\mathrm{CFT}$). $\mathrm{AdS}/\mathrm{CFT}$ posits an equivalence between a gravitational theory and a strongly interacting field theory, allowing the spectrum of applications to be extended to problems in hydrodynamics, condensed matter physics, and nuclear physics. The final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles.

中文翻译：

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爱因斯坦方程的大极限

综述了采用爱因斯坦方程的大尺寸极限的最新进展。尽管讨论了包括量子引力效应的各种扩展，但是大多数分析都是经典的，并且涉及存在黑洞视界的情况。这篇综述由两个主要部分组成：第一部分是在这个大尺寸限制内讨论黑洞的一般方面和有效的膜理论，第二部分是对该限制在有趣的物理问题上的一系列应用。第一部分包括对准标准模态的讨论，自然地可以得出描述近似水平几何的有效流体动力学方程的描述。这些有效理论有两种主要的方法，一种是完全协变方法，另一种是部分固定的方法，相互讨论。在第二部分中，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 Sitter /共形场理论对应关系（$\mathrm{广告}/\mathrm{CFT}$）。 $\mathrm{广告}/\mathrm{CFT}$引力理论与强相互作用场论之间存在等价关系，从而使应用范围扩展到流体力学，凝聚态物理和核物理中的问题。这篇评论的最后一部分简短介绍了进一步的有希望的方向，这些方向迄今为止还很少有已发表的研究文章。