Black Diamonds at Brane Junctions

TL;DR

This paper explores black holes in brane-world models with extra dimensions, presenting an exact solution for black p-branes that induce Schwarzschild black holes on the brane, and discusses their stability and geometric deformation.

Contribution

It introduces an exact solution for black p-branes in higher-dimensional anti-de Sitter spacetime that induce Schwarzschild black holes on the brane-world, and analyzes their stability and geometric shape.

Findings

Black p-branes induce Schwarzschild solutions on the brane.

The solutions are unstable to Gregory-Laflamme instability.

Deformed horizons resemble black diamonds or polyhedra depending on extra dimensions.

Abstract

We discuss the properties of black holes in brane-world scenarios where our universe is viewed as a four-dimensional sub-manifold of some higher-dimensional spacetime. We consider in detail such a model where four-dimensional spacetime lies at the junction of several domain walls in a higher dimensional anti-de Sitter spacetime. In this model there may be any number p of infinitely large extra dimensions transverse to the brane-world. We present an exact solution describing a black p-brane which will induce on the brane-world the Schwarzschild solution. This exact solution is unstable to the Gregory-Laflamme instability, whereby long-wavelength perturbations cause the extended horizon to fragment. We therefore argue that at late times a non-rotating uncharged black hole in the brane-world is described by a deformed event horizon in p+4 dimensions which will induce, to good approximation, the Schwarzschild solution in the four-dimensional brane world. When p=2, this deformed horizon resembles a black diamond and more generally for p>2, a polyhedron.