Moduli space of supersymmetric black holes

The classification of higher dimensional stationary black hole solutions to the Einstein equations is a major open problem in higher dimensional general relativity. Besides being of intrinsic mathematical interest, this problem also has important applications in modern studies of high energy physics, quantum gravity and string theory. This project will investigate the classification of asymptotically flat, supersymmetric black hole solutions to five dimensional minimal supergravity. These are particular interest in string theory. A rich moduli space of solutions is expected corresponding to black holes with exotic horizon topologies (lens space) and non-trivial topology in the domain of outer communication (2-cycles). The first part of the project will be to classify supersymmetric black holes with biaxial symmetry by combining supersymmetry with the methods used for axisymmetric solutions in general relativity. The second part of the project will be to investigate supersymmetric black holes with a single axial symmetry and a particular aim will be to construct the first regular examples. A solution to these problems would be a valuable contribution to the black hole classification program.