Microstate geometries are smooth, time-independent, asymptotically flat, horizon free solutions of type IIB supergravity. In the fuzzball conjecture, they are supposed to provide a geometrical description of certain black hole microstates. Some non-BPS microstate geometries have an ergoregion, which implies that they suffer a linear instability. BPS microstate geometries have no ergoregion so one might expect linear stability. However, I will argue that they suffer a nonlinear instability.

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Please note the unusual time!