Small Black Holes on Branes: Is the horizon regular or singular ?

TL;DR

This paper examines whether small black holes on branes in the Randall-Sundrum model have regular horizons or naked singularities, using perturbative expansions and weak field approximations.

Contribution

It demonstrates that first-order solutions suggest a singular horizon, while a regular horizon solution involves half-integer powers in the mass expansion.

Findings

First-order weak field solution indicates a singular horizon.

A regular horizon solution involves half-integer powers of mass.

Perturbative approach reveals the nature of the horizon in brane black holes.

Abstract

We investigate the following question: Consider a small mass, with $\epsilon$ (the ratio of the Schwarzschild radius and the bulk curvature length) much smaller than 1, that is confined to the TeV brane in the Randall-Sundrum I scenario. Does it form a black hole with a regular horizon, or a naked singularity? The metric is expanded in $\epsilon$ and the asymptotic form of the metric is given by the weak field approximation (linear in the mass). In first order of $\epsilon$ we show that the iteration of the weak field solution, which includes only integer powers of the mass, leads to a solution that has a singular horizon. We find a solution with a regular horizon but its asymptotic expansion in the mass also contains half integer powers.