Perturbations around the near horizon limit of charged Randall Sundrum black holes

TL;DR

This paper extends previous work on extremal charged black holes in the Randall-Sundrum model by analyzing metric corrections near the horizon, showing that large black holes approximate 4D Reissner-Nordström solutions.

Contribution

It provides a detailed metric expansion around the near horizon limit of charged black holes in the Randall-Sundrum model, including correction terms up to second order.

Findings

Corrected bulk metric remains sliceable by a brane despite symmetry breaking.

Induced brane metric matches 4D Reissner-Nordström solution for large black holes.

Agreement with 4D General Relativity is confirmed in the large black hole limit.

Abstract

In a previous paper we determined the near horizon limit of an extremal brane world black hole, charged with respect to a Maxwell field on the brane, in the single brane Randall-Sundrum model. This paper is largely an extension of that work. The same black hole is considered. A metric expansion around the near horizon limit is set up and the correction terms of the first two subleading orders are determined. It is found that the corrected bulk metric can still be sliced by a brane even though the $Ads_{2}$ symmetry of the near horizon metric is broken by correction terms. The induced metric on the brane is determined to second correction order and compared with the predictions of 4d General Relativity. It is found that large black holes asymptote the extremal Reissner Nordstr\"om solution and thus agreement with 4d General Realtivity is obtained in this limit.