Possible Extensions of the 4-d Schwarzschild Horizon in the Brane World

TL;DR

This paper investigates the possible shapes of black hole horizons in brane world models, showing that the horizon's extension off the brane is restricted to a tubular form due to Einstein equations and the bulk geometry.

Contribution

It demonstrates that in the Randall-Sundrum brane world, the off-brane extension of a Schwarzschild horizon must be tubular, not pancake-shaped, under certain conditions.

Findings

Off-brane Schwarzschild horizons are tubular in shape.

Pancake-shaped horizons are not compatible with the model.

Tubular horizons are absent when viewed from the AdS boundary.

Abstract

We show that, in the absence of matter in the bulk, the Einstein equations and the Gauss-normal form of the metric place stringent restrictions on the form of the event horizon in a brane world. As a consequence, the off-brane extension of the standard 4-D Schwarzschild horizon in the Randall-Sundrum $AdS_5$ spacetime, as it is viewed from the brane can only be of a tubular shape, instead of a pancake shape. When it is viewed from the $AdS_5$ horizon, such a tubular horizon is absent.