Brane World in a Topological Black Hole Bulk

TL;DR

This paper explores the behavior of a static brane within a topological black hole background across various dimensions, revealing conditions for brane placement and connections to Randall-Sundrum models.

Contribution

It provides new solutions for branes in topological black hole backgrounds, including conditions for brane tension and links to known models in specific limits.

Findings

Brane position coincides with the horizon for hyperbolic horizons.

Brane tension vanishes at the black hole's minimum negative mass.

Massless Randall-Sundrum mode recovered at large black hole mass.

Abstract

We consider a static brane in the background of a topological black hole, in arbitrary dimensions. For hyperbolic horizons, we find a solution only when the black hole mass assumes its minimum negative value. In this case, the tension of the brane vanishes, and the brane position coincides with the location of the horizon. For an elliptic horizon, we show that the massless mode of Randall-Sundrum is recovered in the limit of large black hole mass.