Instability of nonsupersymmetric smooth geometries

Recently certain nonsupersymmetric solutions of type IIb supergravity were constructed V. Jejjala, O. Madden, S. F. Ross, and G. Titchener, Phys. Rev. D 71, 124030 (2005)., which are everywhere smooth, have no horizons and are thought to describe certain non-Bogomolnyi-Prasad-Sommerfield microstates of the D1-D5 system. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the end point of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's fuzzball proposal.