Moduli space of supersymmetric solitons and black holes in five dimensions

TL;DR

This paper classifies all asymptotically flat, supersymmetric, biaxisymmetric solutions in five-dimensional minimal supergravity, revealing a large moduli space of black holes and solitons with specific horizon topologies.

Contribution

It provides a complete classification of supersymmetric soliton and black hole solutions, including their horizon topologies and moduli space structure, in five-dimensional minimal supergravity.

Findings

Horizon topology must be S^3, S^1 x S^2, or lens space L(p,1).

Constructed general solutions for each rod structure.

Identified a large moduli space of solutions with noncontractible 2-cycles.

Abstract

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.