Moduli space of supersymmetric black holes in five dimensions

Abstract

This thesis presents a classification of all asymptotically at, supersymmetric and biaxisymmetric (i.e. possessing a U(1)2-symmetry) soliton and black hole solutions to five-dimensional minimal supergravity. In particular, by combining local constraints from supersymmetry of the solutions with global constraints for stationary and bi-axisymmetric spacetimes, we show that any solution must be multi-centred with a Gibbons{Hawking base. We also find a refinement of the allowed horizon topologies of this class of solutions, to one of S3, S1 X S2 or a lens space L(p; 1). We construct the general, smooth solution associated with each possible rod structure, thereby finding a large moduli space of black hole spacetimes with noncontractible 2-cycles in the domain of outer communication. This includes examples for each of the allowed horizon topologies. In the absence of a black hole we obtain a classification of the known "bubbling" soliton spacetimes. We then move on to a systematic analysis of the subclass of three-centred solutions contained in the constructed moduli space, focusing on the special case of single black hole solutions. This class is composed of seven regular black hole solutions. We find that four of these can have the same conserved charges as the original spherical, supersymmetric black hole, the BMPV solution. These consist of a black lens with L(3; 1) horizon topology and three distinct families of spherical black holes with nontrivial topology outside the horizon. The former provides the first example of a nonspherical black hole with the same conserved charges as the BMPV black hole. Moreover, of these four solutions, three can have a greater entropy than the BMPV black hole near the BMPV upper spin bound. One of these is a previously known spherical black hole with nontrivial topology; the other two are new examples of a spherical black hole with nontrivial topology and an L(3; 1) black lens.