Harvey Reall: Research

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Higher dimensional General Relativity

This project was supported by a grant from the European Research Council which ran from 2011 to 2016.

The study of General Relativity (GR) in more than four spacetime dimensions is motivated by string theory e.g. via the gauge/gravity correspondence or scenarios that predict black hole production at the Large Hadron Collider, and by purely mathematical considerations.

It is known that higher-dimensional GR exhibits qualitative differences from 4d GR, especially for black holes, e.g. there exist "black ring" solutions describing rotating, donut-shaped black holes. It is likely that there are many other interesting solutions that remain to be discovered. This project will consider the following topics in higher-dimensional GR:

1. Development of new methods for solving the Einstein equation.
2. Classical stability of rotating black holes: recent work indicates that some such black holes are unstable but only special cases have been considered so far, owing to the complexity of the equations. New techniques will be developed to overcome this problem and determine which black holes are unstable.
3. Classification of black hole solutions: What data is required to specify uniquely black hole solutions? What are the allowed topologies and symmetries of black holes?