Black Hole Thermodynamics and Hamilton-Jacobi Counterterm

TL;DR

This paper reviews the Hamilton-Jacobi counterterm approach in dilaton gravity, explores black hole thermodynamics and semi-classical corrections, and applies these concepts to various black hole solutions across different dimensions and theories.

Contribution

It introduces a universal Hamilton-Jacobi counterterm for dilaton gravity and extends the analysis to diverse black hole configurations and formulations.

Findings

Derived the counterterm in the Cartan formulation.

Analyzed thermodynamics of spherically symmetric black holes.

Discussed semi-classical corrections in black hole physics.

Abstract

We review the construction of the universal Hamilton-Jacobi counterterm for dilaton gravity in two dimensions, derive the corresponding result in the Cartan formulation and elaborate further upon black hole thermodynamics and semi-classical corrections. Applications include spherically symmetric black holes in arbitrary dimensions with Minkowski- or AdS-asymptotics, the BTZ black hole and black holes in two-dimensional string theory.