Thermodynamic Phase Transitions and Quantum Entropy Corrections in the Simpson-Visser Regular Black Hole

TL;DR

This paper investigates the thermodynamic properties and quantum entropy corrections of Simpson-Visser regular black holes, revealing phase transitions and stability features that influence black hole evaporation and end-states.

Contribution

It introduces a detailed thermodynamic analysis of Simpson-Visser regular black holes, including quantum entropy corrections, highlighting the thermodynamic significance of singularity resolution.

Findings

Identifies a critical phase transition with discontinuous heat capacity.

Derives quantum corrections to black hole entropy beyond the semiclassical limit.

Provides insights into the stability and end-state of evaporating regular black holes.

Abstract

Regular black holes offer a compelling framework to explore the consequences of resolving the central singularity of standard black holes. Using the Simpson-Visser "black-bounce" geometry as an elegant, analytically tractable framework, we explore the intricate thermodynamic behavior in such models. We demonstrate that this regular spacetime exhibits a critical instability, marked by a phase transition where the heat capacity is discontinuous. This transition signals a fundamental change in the black hole's evaporation state, which depends on the regularization parameter. Pushing beyond the semiclassical limit, we then derive the leading-order quantum corrections to the entropy via the Hamilton-Jacobi tunneling formalism. Our analysis provides a refined statistical basis for the entropy of non-singular spacetimes and offers a quantitative analysis of the nature of the black hole end-state. These results reveal that singularity resolution is not merely a geometric modification but a profound thermodynamic event, with direct implications for the stability and ultimate fate of evaporating black holes.