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

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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.