Black Hole Chemistry Knows Extra Dimensions

TL;DR

This paper investigates how extra dimensions influence black hole thermodynamics and phase transitions in an 8-dimensional Einstein-Yang-Mills-Maxwell framework, revealing their impact on black hole size and thermodynamic properties.

Contribution

It demonstrates the effect of extra dimensions on black hole phase transitions and thermodynamics in a reduced 4D model derived from higher-dimensional theory.

Findings

Extra dimensions affect the thermodynamic pressure and phase structure of black holes.

The size of extra dimensions is conjugate to black hole horizon size in thermodynamics.

Extra dimensions influence the viable black hole sizes in anti-de Sitter spacetime.

Abstract

: In this note, we study an extra dimension effect on the black hole chemistry in the 8-dimensional Einstein-Yang-Mills-Maxwell theory. The base spacetime contains 4- dimensional compact manifolds and an instanton on top of those. We demonstrate how the extra dimensions affect the phase transition and viable black hole sizes in the 4-dimensional Einstein frame through the black hole chemistry. We focus on asymptotically anti-de Sitter spacetimes for the effective 4-dimensional model obtained by a dimensional reduction. The extra-dimension size determines thermodynamic pressure, and the thermodynamic volume is roughly the horizon size of black holes. Thus, the extra dimension and black hole sizes are related as a conjugate pair of thermodynamic variables.