Thermodynamic Properties of Small Localized Black Holes

TL;DR

This paper analyzes the thermodynamic properties of small localized black holes in a braneworld scenario, revealing smooth deviations from five-dimensional Schwarzschild black holes and similarities with 4D braneworld solutions.

Contribution

It provides a quantitative analysis of thermodynamic behavior of numerically obtained localized black hole solutions in a braneworld context, extending previous numerical methods.

Findings

Localized black holes deviate smoothly from 5D Schwarzschild black holes.

Thermodynamic behavior shows similarities with 4D braneworld solutions.

Numerical solutions describe small localized black holes accurately.

Abstract

In a previous paper, we developed a numerical method to obtain a static black hole localized on a 3-brane in the Randall-Sundrum infinite braneworld, and presented examples of numerical solutions that describe small localized black holes. In this paper we quantitatively analyze the behavior of the numerically obtained black hole solutions, focusing on thermodynamic quantities. The thermodynamic relations show that the localized black hole deviates smoothly from a five-dimensional Schwarzschild black hole, which is a solution in the limit of a small horizon radius. We compare the thermodynamic behavior of these solutions with that of the exact solution on the 2-brane in the 4D braneworld. We find similarities between them.