Euclidean and Hamiltonian thermodynamics for regular black holes

TL;DR

This paper explores the thermodynamics of Hayward regular black holes across different spacetimes using Euclidean and Hamiltonian methods, revealing consistent temperature definitions, phase behavior, and the absence of Hawking-Page transitions.

Contribution

It introduces an effective temperature for regular black holes, demonstrates consistency between Euclidean and Hamiltonian approaches, and analyzes phase structure with quantum gravity considerations.

Findings

Effective temperature differs from surface gravity-based temperature.

Standard mean-field critical behavior observed with cosmological constant as pressure.

No Hawking-Page transition occurs, possibly due to quantum gravity effects.

Abstract

We investigate the thermodynamic properties of the Hayward regular black hole using both Euclidean path integral and Hamiltonian methods, in asymptotically anti-de Sitter, Minkowski, and de Sitter spacetimes. With the inclusion of matter fields which act as a source for the regular black hole geometry, an effective temperature emerges that differs from the conventional definition related to the Killing surface gravity. We posit that this temperature is the appropriate choice for studying thermodynamic phenomena, by demonstrating consistency between the Euclidean and Hamiltonian formulations in the appropriate limits. We examine the thermodynamic properties and phase structure of the Hayward black hole in the canonical ensemble and show that, counter to some earlier indications, standard mean-field theory critical behavior is observed when the cosmological constant is treated as a thermodynamic pressure. We note the absence of a Hawking-Page transition, and conjecture that quantum gravity corrections which are suitably strong to regulate the Schwarzschild singularity generically prevent the transition from occurring. We also show that the Smarr relation remains linear in all cases, despite the absence of a linearity proof for nonlinear electrodynamic theories with nonsymmetry inheriting fields.