Quest for Localized 4-D Black Holes in Brane Worlds

TL;DR

This paper explores the theoretical possibility of localized four-dimensional black holes in brane world models, finding that exotic matter distributions are necessary to support such solutions and prevent black string behavior.

Contribution

It introduces a new approach to obtaining localized black hole solutions in brane worlds by analyzing matter requirements and proposing an exotic matter distribution.

Findings

Localized black hole solutions require exotic, shell-like matter distributions.

Conventional matter cannot support the necessary dependence of the metric on the extra dimension.

The solutions avoid black string behavior and have well-defined spacetime near the AdS horizon.

Abstract

We investigate the possibility of obtaining localized black hole solutions in brane worlds by introducing a dependence of the four-dimensional line--element on the extra dimension. An analysis, performed for the cases of an empty bulk and of a bulk containing either a scalar or a gauge field, reveals that no conventional type of matter can support such a dependence. Considering a particular ansatz for the five-dimensional line--element that corresponds to a black hole solution with a ``decaying'' horizon, we determine the bulk energy--momentum tensor capable of sustaining such a behaviour. It turns out that an exotic, shell-like distribution of matter is required. For such solutions, the black hole singularity is indeed localized near the brane and the spacetime is well defined near the AdS horizon, in contrast to the behaviour found in black string type solutions.