Quasilocal Thermodynamics of Dilaton Gravity coupled to Gauge Fields

TL;DR

This paper develops a framework for calculating quasilocal thermodynamic quantities and conserved charges in Einstein-Hilbert-Dilaton gravity coupled with various gauge fields, including applications to black hole entropy and thermodynamics.

Contribution

It introduces methods to compute quasilocal quantities and conserved charges for gravity coupled with Abelian and non-Abelian gauge fields, extending black hole thermodynamics.

Findings

Derived expressions for energy and angular momentum of gauge fields.

Established a form of the first law of black hole thermodynamics with these gauge fields.

Provided a micro-canonical entropy formula for stationary black holes.

Abstract

We consider an Einstein-Hilbert-Dilaton action for gravity coupled to various types of Abelian and non-Abelian gauge fields in a spatially finite system. These include Yang-Mills fields and Abelian gauge fields with three and four-form field strengths. We obtain various quasilocal quantities associated with these fields, including their energy and angular momentum, and develop methods for calculating conserved charges when a solution possesses sufficient symmetry. For stationary black holes, we find an expression for the entropy from the micro-canonical form of the action. We also find a form of the first law of black hole thermodynamics for black holes with the gauge fields of the type considered here.