On a general class of brane-world black holes

TL;DR

This paper develops a general framework for black hole metrics in brane-world scenarios, unifying various types of black holes and wormholes using solutions to Einstein's equations with an arbitrary metric function.

Contribution

It introduces a broad class of black hole solutions based on the trace of Einstein's equations, encompassing regular, extremal, and wormhole geometries with flexible boundary conditions.

Findings

Families of solutions unify different black hole types and wormholes.

Horizons can be simple, double, or of higher order depending on conditions.

Applications to brane-world models with solutions extendable into 5D bulk.

Abstract

We use the general solution to the trace of the 4-dimensional Einstein equations for static, spherically symmetric configurations as a basis for finding a general class of black hole (BH) metrics, containing one arbitrary function $g_{tt} = A(r)$ which vanishes at some $r = r_h > 0$, the horizon radius. Under certain reasonable restrictions, BH metrics are found with or without matter and, depending on the boundary conditions, can be asymptotically flat or have any other prescribed large $r$ behaviour. It is shown that this procedure generically leads to families of solutions unifying non-extremal globally regular BHs with a Kerr-like global structure, extremal BHs and symmetric wormholes. Horizons in space-times with zero scalar curvature are shown to be either simple or double. The same is generically true for horizons inside a matter distribution, but in special cases there can be horizons of any order. A few simple examples are discussed. A natural application of the above results is the brane world concept, in which the trace of the 4D gravity equations is the only unambiguous equation for the 4D metric, and its solutions can be continued into the 5D bulk according to the embedding theorems.