Six-dimensional localized black holes: numerical solutions

TL;DR

This paper presents improved numerical solutions for six-dimensional localized black holes in Randall-Sundrum braneworlds, revealing thermodynamic transitions, horizon geometry features, and implications for gravity recovery on the brane.

Contribution

It advances numerical methods to analyze large 6D black holes, uncovering their thermodynamic behavior and horizon geometry, extending previous smaller black hole studies.

Findings

Thermodynamic transition from 6D Schwarzschild to black string type.

Negative specific heat of localized black holes.

Flattened horizon geometries with negative intrinsic curvature near the brane.

Abstract

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature $\mathcal{T} \approx 1/2\pi \ell$, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes.