Localized brane-world black hole analytically connected to an AdS$_5$ boundary

TL;DR

This paper constructs an analytic model of a five-dimensional brane-world black hole with a localized horizon, connecting the bulk geometry to the boundary, and showing it can be supported without matter on the brane.

Contribution

It provides the first first-principles analytic construction of a localized brane-world black hole with a pancake-shaped horizon and a bulk supported by anisotropic fluid.

Findings

Black hole singularity is confined to the brane.

Event horizon has a pancake shape.

Bulk geometry is effectively AdS$_5$ outside the horizon.

Abstract

We construct from first principles the geometry of an analytic, exponentially localized five-dimensional brane-world black hole. The black-hole singularity lies entirely on the 3-brane, while the event horizon is shown to have a pancake shape. The induced line-element on the brane assumes the form of the Schwarzschild solution while the bulk geometry is effectively AdS$_5$ outside the horizon. The derived geometry is supported by an anisotropic fluid in the bulk described only by two independent components, the energy density and tangential pressure, whereas no matter needs to be introduced on the brane for its consistent embedding in the bulk.