Black Holes and Instabilities of Negative Tension Branes

TL;DR

This paper investigates the collision between a black hole and a negative tension brane in 2+1 dimensions, revealing a new classical instability characterized by a catastrophic singularity that challenges the generalized second law of thermodynamics.

Contribution

It demonstrates a novel instability of negative tension branes in classical general relativity, showing that such configurations can lead to space-time singularities instead of stable equilibrium states.

Findings

Horizon area shrinks without gravitational radiation

Collision leads to a big crunch-like singularity

Challenges the stability of negative tension brane models

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 $\Omega >1$ FRW space-times. In the context of classical general relativity, our result demonstrates a new instability of constructions with negative tension branes.