Geometro-thermodynamics of tidal charged black holes

TL;DR

This paper investigates the thermodynamics and geometric properties of tidal charged black holes in brane-world scenarios, comparing them to Reissner-Nordström black holes, and constrains their parameters based on thermodynamic stability and gravitational radiation limits.

Contribution

It provides a detailed thermodynamic analysis of tidal charged black holes, highlighting differences from classical black holes and constraining the tidal charge range using gravitational wave data.

Findings

Heat capacity diverges at specific parameter points without phase transitions.

Thermodynamic state spaces differ, implying different underlying statistical models.

The negative tidal charge range is thermodynamically favored and constrained by gravitational radiation limits.

Abstract

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q, an imprint of the 5-dimensional Weyl curvature. For q>0 they are formally identical to the Reissner-Nordstr\"om black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner-Nordstr\"om black hole. As a similarity, we show that (for q>0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincar\'e stability analysis shows no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.