Are regular black holes from pure gravity classified within the same thermodynamical topology?

TL;DR

This paper investigates whether regular black holes from pure gravity share the same thermodynamical topological classification, revealing universal behaviors and suggesting a common topological category based on their free energy and temperature properties.

Contribution

It introduces a thermodynamical topological framework to classify regular black holes from pure gravity, demonstrating their universal thermodynamic behaviors and potential unified topological class.

Findings

Regular black holes exhibit at least one zero in Hawking temperature at small horizon radius.

Pure gravity regular black holes show universal thermodynamical behaviors.

These black holes likely belong to the same topological class based on thermodynamical topology.

Abstract

Regular black holes, which avoid the essential center singularities, can be constructed through various methods, including nonlinear electrodynamics and quantum corrections. Recently, it was shown that via an infinite tower of higher-curvature corrections, one can obtain different regular black hole solutions in any spacetime dimension $D\geq 5$. Utilizing the concept of thermodynamical topology, we examine these black holes as topological thermodynamic defects, classifying them into distinct topological categories based on their generalized free energy. We find that the Hawking temperature of the black hole has at least one zero point at the small horizon radius limit. Under this fact, the regular black holes generated through the purely gravitational theories exhibit universal thermodynamical behaviors, strongly suggesting they belong to the same topological class. We presents a comprehensive analysis of these properties, providing a clearer understanding of the fundamental nature of regular black holes and their classification within the framework of thermodynamical topology.