IPHT-t13/059 Global Structure of Five-dimensional BPS Fuzzballs

We describe and study families of BPS microstate geometries, namely, smooth, horizon-less 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 mi-crostate 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 S2 × S2 with a “point at infinity ” re-moved. 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. ar X i