Global Structure of Five-dimensional BPS Fuzzballs

TL;DR

This paper constructs and analyzes five-dimensional BPS microstate geometries in supergravity, revealing new topological structures and properties that circumvent previous no-go theorems, and explaining why some solitons violate BPS bounds.

Contribution

It introduces a new class of smooth, horizonless microstate geometries with complex topology, modifying the Smarr formula and analyzing ergo-regions, advancing understanding of BPS solutions in supergravity.

Findings

Existence of microstate geometries with connected sum topology of S^2 x S^2

Presence of evanescent ergo-regions in solutions

Resolution of the spin structure puzzle for solitons

Abstract

We describe and study families of BPS microstate geometries, namely, smooth, horizonless asymptotically-flat solutions to supergravity. We examine these solutions from the perspective of earlier attempts to find solitonic solutions in gravity and show how the microstate geometries circumvent the earlier "No-Go" theorems. In particular, we re-analyse the Smarr formula and show how it must be modified in the presence of non-trivial second homology. This, combined with the supergravity Chern-Simons terms, allows the existence of rich classes of BPS, globally hyperbolic, asymptotically flat, microstate geometries whose spatial topology is the connected sum of N copies of S^2 x S^2 with a "point at infinity" removed. These solutions also exhibit "evanescent ergo-regions," that is, the non-space-like Killing vector guaranteed by supersymmetry is time-like everywhere except on time-like hypersurfaces (ergo-surfaces) where the Killing vector becomes null. As a by-product of our work, we are able to resolve the puzzle of why some regular soliton solutions violate the BPS bound: their spactimes do not admit a spin structure.