Thick brane solutions and topology change transition on black hole backgrounds

TL;DR

This paper provides exact numerical solutions for static, axisymmetric thick branes on black hole backgrounds, revealing topology change transitions and overcoming perturbative limitations in higher dimensions.

Contribution

It introduces a non-perturbative, numerical approach to analyze thick branes on black hole backgrounds, including topology change transitions, for arbitrary dimensions.

Findings

Exact numerical solutions for thick branes on black hole backgrounds.

Demonstration of topology change transition in 5D brane within 6D bulk.

Identification of perturbative approach limitations in higher dimensions.

Abstract

We consider static, axisymmetric, thick brane solutions on higher dimensional, spherically symmetric black hole backgrounds. It was found recently [1], that in cases when the thick brane has more than 2 spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a non-perturbative approach. In the present paper we provide an exact, numerical solution of the problem both for black hole- and Minkowski type topologies with arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a 5-dimensional brane embedded in a 6-dimensional bulk.