Quest for Localized 4-D Black Holes in Brane Worlds. II : Removing the bulk singularities

TL;DR

This paper explores localized black hole solutions in brane-world models, focusing on horizon-analytic metrics with decaying extra-dimensional dependence, and demonstrates that certain Vaidya-type solutions can be supported by regular bulk matter.

Contribution

It introduces horizon-analytic black hole metrics with decaying extra-dimensional dependence and shows they can be supported by regular bulk matter without additional singularities.

Findings

Vaidya line-element provides a natural localized black hole solution

The 5D spacetime retains RS-Schwarzschild topology

Minimal bulk energy-momentum tensor supports the solutions

Abstract

We analyze further the possibility of obtaining localized black hole solutions in the framework of Randall-Sundrum-type brane-world models. We consider black hole line-elements analytic at the horizon, namely, generalizations of the Painleve and Vaidya metrics, which are taken to have a decaying dependence of the horizon on the extra dimension. These backgrounds have no other singularities apart from the standard black hole singularity which is localized in the direction of the fifth dimension. Both line-elements can be sustained by a regular, shell-like distribution of bulk matter of a non-standard form. Of the two, the Vaidya line-element is shown to provide the most attractive, natural choice: despite the scaling of the horizon, the 5D spacetime has the same topological structure as the one of a RS-Schwarzschild spacetime and demands a minimal bulk energy-momentum tensor.