Black holes and instabilities of negative tension branes

Abstract

We consider the collision in $2+1$ dimensions of a black hole and a negative tension brane on an orbifold. Because there is no gravitational radiation in $2+1$ dimensions, the horizon area shrinks when part of the brane falls through. This provides a potential violation of the generalized second law of thermodynamics. However, tracing the details of the dynamical evolution, one finds that it does not proceed from equilibrium configuration to equilibrium configuration. Instead, a catastrophic space-time singularity develops similar to the ``big crunch'' of $\ensuremath{\Omega}>1$ Friedmann-Robertson-Walker space-times. In the context of classical general relativity, our result demonstrates the instability of constructions with negative tension branes.