A topologically flat thick 2-brane on higher dimensional black hole backgrounds

TL;DR

This paper numerically constructs a topologically flat thick 2-brane in higher-dimensional black hole backgrounds, completing the set of solutions and highlighting unique non-analytic features at the axis.

Contribution

It provides the first numerical solution for a thick 2-brane in this context, completing the solution set for arbitrary dimensions and analyzing its unique properties.

Findings

The 2-brane solution is non-analytic at the axis.

Numerical solutions are obtained in the near horizon region.

Comparison with thin brane solutions shows differences due to thickness.

Abstract

We present a numerical solution for a topologically flat 2-dimensional thick brane on a higher dimensional, spherically symmetric black hole background. Present solution is the last, missing part of the complete set of solutions for the thickness corrected brane-black hole problem in arbitrary number of dimensions. We show that the 2-dimensional case is special compared to all the higher dimensional solutions in the topologically Minkowskian family as being non-analytic at the axis of the system. We provide the numerical solution in the near horizon region and make a comparison with the infinitely thin case.