$g_{tt}g_{rr} =-1$ black hole thermodynamics in extended quasi-topological gravity

TL;DR

This paper develops a unified framework for analyzing the thermodynamics of $g_{tt}g_{rr}=-1$ black holes in extended quasi-topological gravity, applicable to various horizon topologies and asymptotics.

Contribution

It introduces an effective 2D dilaton theory approach that links black hole solutions to a generalized first law and Wald entropy in extended quasi-topological gravity.

Findings

Provides a method to compute thermodynamic mass from a generating function.

Applies to both singular and regular black holes with different asymptotics.

Unifies thermodynamic analysis across various horizon topologies.

Abstract

We present a unified framework for the discussion of black hole thermodynamics of $d$-dimensional static black holes with spherical, toroidal or compact hyperbolic horizon topology satisfying $g_{tt}g_{rr}=-1$ in Schwarzschild gauge. To that end, we consider any such black hole as a solution to an integrable $2$-dimensional effective dilaton theory and thereby as a vacuum solution to an extended notion of $d$-dimensional quasi-topological gravity. We show that the generating function determining $f(r) = -g_{tt} $ in the integrated equation of motion provides the thermodynamic mass in a generalised first law with entropy computed as the Wald entropy. The framework presented here can be applied to singular and regular black holes with flat or anti-de Sitter asymptotics.