Small Black Holes in Randall-Sundrum type I Scenario

TL;DR

This paper presents an approximation method to analyze small black holes on the TeV brane within the Randall-Sundrum type I model, focusing on near-horizon metric properties using perturbative expansions.

Contribution

It introduces a novel approximation technique for the near-horizon metric of small black holes in the Randall-Sundrum I scenario, combining short-range expansions and linearized gravity.

Findings

Derived the near-horizon metric form for small black holes

Implemented an expansion in the ratio of Schwarzschild radius to bulk curvature length

Provided a solution valid close to the horizon up to first order

Abstract

An approximation method to study the properties of a small black hole located on the TeV brane in the Randall-Sundrum type I scenario is presented. The method enables us to find the form of the metric close to the matter distribution when its asymptotic form is given. The short range solution is found as an expansion in the ratio between the Schwarzschild radius of the black hole and the curvature length of the bulk. Long range properties are introduced using the linearized gravity solution as an asymptotic boundary condition. The solution is found up to first order. It is valid in the region close to the horizon but is not valid on the horizon. The regularity of the horizon is still under study.