Thermodynamics of four-dimensional regular black holes with an infinite tower of regularized curvature corrections

TL;DR

This paper investigates the thermodynamics of four-dimensional black holes derived from higher-curvature gravity theories with an infinite series of curvature corrections, revealing degeneracies and conditions for thermodynamic preference.

Contribution

It introduces a novel analysis of black hole thermodynamics in theories with infinite curvature corrections, highlighting degeneracies and the impact of quadratic terms on stability.

Findings

Planar horizons exhibit thermodynamic degeneracy between regular and non-regular solutions.

Degeneracy persists for spherical horizons without quadratic curvature contributions.

Quadratic curvature terms influence the thermodynamic favorability of regular solutions.

Abstract

We study the thermodynamics of a class of four-dimensional black hole solutions arising from the compactification of a higher-curvature gravity theory featuring an infinite tower of Lovelock-type invariants. For planar horizons, we identify two distinct branches: a regular black hole supported by a nontrivial scalar field and a non-regular general relativity (GR) solution with a trivial scalar profile. Despite their differing geometries, both branches share the same free energy at fixed temperature, revealing a thermodynamic degeneracy naturally linked to the enhanced symmetry and scale invariance of the planar base manifold. In the case of a spherical horizon, even if the scalarized branch is not obtained in closed form, one can see that the degeneracy persists in the absence of the quadratic curvature contribution. On the other hand, if this quadratic term is taken into account, the regular solution may be thermodynamically favored (or not) over the Schwarzschild-AdS solution depending on the values of the coupling constants of the theory.