Thermodynamics of Black Holes in Two (and Higher) Dimensions

TL;DR

This paper develops a comprehensive framework for black hole thermodynamics in two-dimensional dilaton gravity, including an improved action, boundary terms, and analysis of stability, with applications to string theory and higher-dimensional black holes.

Contribution

It introduces an improved action and boundary counterterms for 2D black hole thermodynamics, enabling well-defined semi-classical path integrals and extending methods to higher-dimensional cases.

Findings

The Euclidean path integral is well-defined with the new boundary counterterm.

The Exact String Black Hole admits consistent thermodynamics without external reservoirs.

The approach applies to higher-dimensional black holes like Schwarzschild-AdS and BTZ.

Abstract

A comprehensive treatment of black hole thermodynamics in two-dimensional dilaton gravity is presented. We derive an improved action for these theories and construct the Euclidean path integral. An essentially unique boundary counterterm renders the improved action finite on-shell, and its variational properties guarantee that the path integral has a well-defined semi-classical limit. We give a detailed discussion of the canonical ensemble described by the Euclidean partition function, and examine various issues related to stability. Numerous examples are provided, including black hole backgrounds that appear in two dimensional solutions of string theory. We show that the Exact String Black Hole is one of the rare cases that admits a consistent thermodynamics without the need for an external thermal reservoir. Our approach can also be applied to certain higher-dimensional black holes, such as Schwarzschild-AdS, Reissner-Nordstrom, and BTZ.