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arXiv · 2604.24101

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

Johanna Borissova
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Abstract

We present a unified framework for the discussion of black hole thermodynamics of $d$-dimensional static black holes with spherical 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 a generalised 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.

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Johanna Borissova. 2026-04-27. $g_{tt}g_{rr} =-1$ black hole thermodynamics in general quasi-topological gravity. https://doi.org/10.1103/gbdk-xm4c

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