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General relativity is our best theory to describe the gravitational force. Among one of its most striking predictions is the existence of black holes. The latter are regions of the spacetime from which nothing, even light, can escape. In four spacetime dimensions, the properties of equilibrium black holes are well-understood: they are uniquely specified by their mass and spin, they are spherically shaped, and they are dynamically stable. This last property is very important since it makes them astrophysically relevant as the endpoint of the gravitational collapse of a star. Indeed, according to our current understanding, after a sufficiently massive star has exhausted its nuclear fuel, it has no other option but to collapse and form a black hole. However, black holes contain in their interior singularities where the gravitational force becomes so extreme that general relativity breaks down. It is expected that in these situations a new theory that combines the laws of quantum mechanics with general relativity, namely a theory of quantum gravity, is required.In recent years the study of general relativity in dimensions greater than four has received a lot of attention for various reasons. First, general relativity is contained in string theory and the latter is our best candidate for a theory of quantum gravity. However, its consistency requires more than four spacetime dimensions. Second, according to recent developments, string theory (and hence gravity) in certain spacetimes is equivalent to an ordinary theory of particles, without gravity, in one spacetime dimension less. Typically, in the regime in which string theory reduces to general relativity the corresponding particle physics theory cannot be described by the standard methods in particle physics. Therefore, five-dimensional gravity, and in particular black holes, provide a novel tool to address problems in standard four-dimensional theories of particles. This new tool has proven to be very useful in a variety of contexts. For example, it has been possible to understand some properties of the quark-gluon plasma that is being produced in accelerators (e.g., the LHC). Finally, some theories predict the production of higher dimensional black holes at the LHC. The main goal of my research is to get a better understanding of higher dimensional black holes. To achieve this I propose to: study the dynamical stability of black holes, find new higher dimensional black holes and study the formation of black holes. One novel property that higher dimensional black holes have is that they can become unstable if they spin sufficiently fast. In four dimensions this cannot happen since the spin of a black hole always has an upper bound. However, the details of these instabilities are not fully understood. In my research I will study these instabilities both analytically and numerically. These instabilities typically signal the existence of new black holes. Hence, their study should give us clues about the kinds of black holes that there are and how they are related. Secondly, the general properties of higher dimensional black holes are not fully understood. In particular, it is not even known what kinds of black holes there can be. For instance, doughnut-shaped black holes have been discovered in five dimensions and they explicitly demonstrate that parameters other than the mass and the spin are needed to fully specify the black hole. In my project I will develop methods to systematically find new black holes analytically.Finally, I will use five-dimensional gravity to study the equilibration of the corresponding particle theory. This process cannot be studied analytically by standard methods, but from the gravity side it corresponds to the formation of a black hole. In addition, my results may have implications for the issue of singularity formation in general relativity, which is an interesting mathematical problem in its own right.
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