Characterizing the moduli space of black hole solutions of the Einstein equations

在大尺度上，宇宙及其组成部分，如行星、恒星和星系，都受到引力的支配。我们用来描述这一点的框架是广义相对论。一个抽象的理论如此准确地描述了我们今天才开始观察的现象，这是一项深刻的成就。事实上，最近引力波的发现为我们提供了GR最大胆的预测之一--黑洞的存在的直接证据。这些大质量物体集中在非常小的区域，甚至连光都无法逃脱它们的引力。人们无法逃脱的区域的边界称为事件视界。要描述黑洞产生的极端引力场，GR和量子力学(QM)--成功地描述小尺度宇宙的理论--都需要。将GR和QM整合到一个单一的理论中将使我们能够回答一些大问题，比如宇宙是如何形成的，它将如何演化。正因为如此，黑洞处于理论物理学发展的前沿。黑洞是非常复杂的动态物体，但我们预计它们最终会稳定到平衡状态。在我们熟悉的四维世界中(三个空间方向和一个时间)，GR说这样的黑洞视界是球状的，就像球的表面一样，只用几个参数来描述--它们的质量、自转和电荷。引人注目的是，量子引力理论的主要候选者--弦理论--断言，实际上存在额外的空间方向。我们预计这些额外维度中的一些太小，以至于我们看不到它们；但在大尺度下，其余维度的动力学由大于四个维度的GR控制。我研究的一个长期目标是在这种情况下理解黑洞--也就是确定什么样的视界形状是可能的，以及需要什么物理量来完全确定它们。我最近的工作明确地产生了第二个非球形黑洞的例子，很明显，还有更多的可能性有待发现。在更高维度的GR也允许“孤子”的存在--这些是具有正质量的自引力、无地平线的物体。甚至可以存在同时包含黑洞和孤子的复合态。我的提议旨在使用系统的方法来描述这个丰富的黑洞空间，并确定约束它们物理参数的界限。这项研究应该会对我们理解量子引力做出重大贡献。学生还将接受在许多领域有价值的有用的定量和分析技能的培训。尽管像大多数基础研究一样，这项工作不太可能立即产生应用，但我相信它是值得的，因为它可以帮助我们在最基本的层面上了解自然。

At large scales, the Universe and its constituents, such as planets, stars, and galaxies, are governed by the force of gravity. The framework we use to describe this is general relativity (GR). It is a profound achievement that an abstract theory so accurately describes phenomena that we are only starting to observe today. Indeed, the recent discovery of gravitational waves give us direct evidence of one of GR's boldest predictions - the existence of black holes. These are massive objects concentrated into regions so small that not even light can escape from their pull. The boundary of the region from which one cannot escape is called the event horizon. To describe the extreme gravitational fields produced by black holes, both GR and quantum mechanics (QM) - the theory which successfully describes the Universe at small scales - are needed. Incorporating both GR and QM into a single theory would allow us to answer big questions, such as how the Universe formed and how it will evolve. For this reason, black holes lie at the forefront of developments in theoretical physics. Black holes are very complicated, dynamic objects, but we expect them to eventually settle down to equilibrium. In our familiar four dimensional world (three spatial directions and one time), GR says that such black hole horizons are spherically shaped, like the surface of a ball, and are described by just a few parameters - their mass, spin, and charge. Strikingly, a leading candidate for a theory of quantum gravity, string theory, asserts that in fact there are additional spatial directions. We expect some of these extra dimensions are so small that we cannot see them; but at large scales, the dynamics in the remaining dimensions is governed by GR in dimensions greater than four. A long term goal of my research is achieve an understanding of black holes in this setting - that is, to determine what kinds of horizon shapes are possible and what physical quantities are needed to fully specify them. My recent work has explicitly produced just the second example of a non-spherically-shaped black hole, and it is clear that a greater set of possibilities remains to be discovered. GR in higher dimensions also allows for the existence of `solitons' - these are self-gravitating, horizonless objects with positive mass. There can even be composite states containing both black holes and solitons. My proposal aims to use systematic methods to characterize this rich space of black holes and determine the bounds that constrain their physical parameters. The research should contribute significantly to our understanding of quantum gravity. Students will also receive training in useful quantitative and analytical skills valued in many fields. Even though this work, like most basic research, is unlikely to produce immediate applications, I believe it is worthwhile as it could help us learn about Nature at its most fundamental level.