Stability and Binding Energy of Small Asymptotically Randall-Sundrum Black Holes

TL;DR

This paper analyzes the stability and binding energy of small black holes in the Randall-Sundrum model, revealing stable black holes on the brane and a new unstable off-brane black hole solution, using analytical variational methods.

Contribution

It provides the first analytical study of black hole stability and binding energy in the RS2 scenario, including a novel off-brane black hole solution.

Findings

Small black holes are gravitationally bound and stable on the brane.

A new static off-brane black hole solution is identified, which is unstable.

Black hole stability is analyzed using a variational principle on initial data.

Abstract

We study the binding of a small black hole to a positive-tension brane in the second Randall-Sundrum scenario (RS2) with orbifold symmetry. We find that a small black hole on the brane has substantial gravitational binding energy to the brane, and is stable against escaping into the bulk. This result can be applied in other models with an orbifold-symmetric brane. We also find a novel static black hole, which is completely localized off the brane and is unstable against translations transverse to the brane. Our results are obtained analytically by applying a variational principle to black hole initial data. This paper is the second in a series on asymptotically RS black holes.