Small localized black holes in a braneworld: Formulation and numerical method

TL;DR

This paper develops a numerical method to find small localized black hole solutions in a braneworld scenario, revealing their properties and transition from five-dimensional Schwarzschild black holes.

Contribution

It introduces a new numerical approach to construct localized black holes in the Randall-Sundrum braneworld and explores their characteristics.

Findings

Localized black holes with small horizon radius are numerically constructed.

Black holes transition smoothly from 5D Schwarzschild solutions as size decreases.

Difficulty arises in finding solutions for larger horizon radii.

Abstract

No realistic black holes localized on a 3-brane in the Randall-Sundrum infinite braneworld have been found so far. The problem of finding a static black hole solution is reduced to a boundary value problem. We solve it by means of a numerical method, and show numerical examples of a localized black hole whose horizon radius is small compared to the bulk curvature scale. The sequence of small localized black holes exhibits a smooth transition from a five-dimensional Schwarzschild black hole, which is a solution in the limit of small horizon radius. The localized black hole tends to flatten as its horizon radius increases. However, it becomes difficult to find black hole solutions as its horizon radius increases.