Moduli space of supersymmetric solitons and black holes in five dimensions

We determine all asymptotically flat, supersymmetric and biaxisymmetric soliton and black hole solutions to five dimensional minimal supergravity. In particular, we show that the solution must be a multi-centred solution with a Gibbons-Hawking base. The proof involves combining local constraints from supersymmetry with global constraints for stationary and biaxisymmetric spacetimes. This reveals that the horizon topology must be one of S^3, S^1 x S^2 or a lens space L(p,1), thereby providing a refinement of the allowed horizon topologies. We construct the general smooth solution for each possible rod structure. We find a large moduli space of black hole spacetimes with noncontractible 2-cycles for each of the allowed horizon topologies. In the absence of a black hole we obtain a classification of the known `bubbling' soliton spacetimes.