Brane-World Black Holes in Randall-Sundrum Models

TL;DR

This paper investigates black hole solutions in Randall-Sundrum brane-world models within anti-de Sitter spacetimes, deriving explicit metrics and connecting brane gravity to known effective actions.

Contribution

It provides explicit brane-world black hole solutions using a modified RS metric ansatz and links brane gravity to the Polyakov action in two dimensions.

Findings

Derived black cigar solutions compatible with previous models

Connected brane Ricci-flat conditions to effective gravity

Showed effective brane gravity in 2D is described by the Polyakov action

Abstract

We study brane-world black holes from Randall-Sundrum(RS) models in ($D+1$)-dimensional anti-de Sitter spacetimes. The solutions are directly obtained by using a slightly modified RS metric ansatz in $D+1$ dimensions. The metric of the brane world can be described by the Schwarzschild solution promoted to the black cigar solution in $D+1$ dimensions, which is compatible with the recently suggested black cigar solution for D=4. Furthermore, we show that the Ricci flat condition for the brane can be easily derived from the effective gravity defined on the brane by using the RS dimensional reduction. Especially, it is shown that in two dimensions the effective gravity on the brane is described by the Polyakov action.