Black Holes in Supergravity

Black holes are widely considered to be the most important objects for studying quantum gravity. In the context of string theory, which is the most promising approach to quantum gravity, they have been a key area of study. String theory has provided significant insights into the physics of black holes. Following Hawking's discovery that black holes are thermodynamical objects, which have an associated entropy, a derivation of the entropy of certain types of black holes has been constructed, using techniques in string theory. The study of black holes in string theory is a very active field of research, and there remains much to be understood. I propose to systematically investigate properties of black hole solutions of supergravity theories. Supergravity theories are extensions of Einstein's gravity, and can be used to describe the low energy limit of string theory. Supersymmetric solutions of these theories possess Killing spinors. The existence of Killing spinors imposes constraints on the geometry of the solution, such as additional symmetries, which enable them to be classified. Supersymmetry has also been particularly important in generating new and interesting solutions, including new black holes. I have previously worked on a number of projects classifying five-dimensional supersymmetric black holes, and finding new solutions. Higher dimensional black holes are particularly interesting because the uniqueness theorems, originally formulated in four dimensions, break down in higher dimensions. For example, in five dimensions there is a black ring solution, which has an annular event horizon, in contrast to the five dimensional black hole which has a spherical event horizon. At present, relatively little is known about the generic structure of black hole solutions in ten and eleven dimensional supergravity, and it is expected that there will be many examples of interesting black objects in these theories, with novel event horizon structures. I have recently developed new techniques in order to investigate the structure of such black holes. I have successfully applied these to investigate the geometry of the region near to the event horizon of supersymmetric black holes in a relatively simple type of ten-dimensional supergravity theory, called heterotic supergravity, and a complete and systematic classification of these solutions has been obtained. I intend to extend this analysis and develop new methods to classify all supersymmetric black hole solutions in more complicated ten and eleven dimensional supergravity theories. The analysis will begin with the assumption that the whole black hole geometry is supersymmetric, not only the region near to the horizon. This imposes more conditions on the geometry. Having classified these geometries, I will extrapolate the solutions away from the near-horizon limit to construct the full black hole solutions. This analysis is particularly well suited for constructing black holes with zero surface temperature. I will then construct a classification of the geometry of the event horizon of black holes which are supersymmetric in the region near to the horizon, but are not supersymmetric away from this region. A small number of examples of these solutions are currently known, and it would be interesting to systematically investigate this type of black hole. This research will provide insights into the geometry and the physics of new black holes. In particular, as has been the case with other types of black hole constructed in string theory, it may be possible to understand the entropy of these black holes using string theory techniques. Recently, it has also been conjectured that some types of superconductors may be described by certain types of black hole. The physical properties of the region near to the event horizon of the black hole play an important role in this description. It is therefore of interest to understand black hole solutions in supergravity.