Quailocal Formalism for Dilaton Gravity with Yang-Mills Fields

TL;DR

This paper develops a quasilocal formalism for dilaton gravity coupled with Yang-Mills fields, enabling the definition of conserved quantities and thermodynamic relations for symmetric solutions with black holes.

Contribution

It introduces a novel quasilocal approach based on Brown and York's method for analyzing dilaton gravity with gauge fields, including thermodynamic laws.

Findings

Defined conserved quantities like mass, angular momentum, and charge for symmetric solutions.

Established a quasilocal first law of thermodynamics for static black hole systems.

Presented a micro-canonical action framework for these gravitational systems.

Abstract

We present a quasilocal formalism, based on the one proposed by Brown and York, for dilaton gravity with Yang-Mills fields. For solutions possessing sufficient symmetry, we define conserved quantities such as mass, angular momentum, and charge. We also present a micro-canonical action and use it to arrive at a quasilocal version of the first law of thermodynamics for static systems containing a black hole.