Horizon entanglement area law from regular black hole thermodynamics

TL;DR

This paper explores the thermodynamics of regular black holes using quantum entanglement concepts, revealing proportional relationships between entanglement entropy, energy, and classical black hole thermodynamic quantities, and analyzing stability and phase transitions.

Contribution

It introduces a quantum entanglement framework to analyze regular black hole thermodynamics, linking entanglement measures to classical entropy and energy, and distinguishes between singular and regular solutions.

Findings

Entanglement entropy is proportional to Bekenstein-Hawking entropy.

Entanglement energy scales with Komar energy.

Heat capacity analysis indicates stability conditions and phase transitions.

Abstract

We investigate the thermodynamics of regular black hole configurations via quantum analogs of entropy and energy -- namely, the entanglement entropy and entanglement energy -- near the event horizon of Bardeen and Hayward black holes. Following standard approaches, we introduce a quantum scalar field propagating in such black hole spacetimes and discretize the field degrees of freedom on a lattice of spherical shells. We observe that, at leading order, the entanglement entropy associated with the scalar field is proportional to Bekestein-Hawking entropy, while the corresponding entanglement energy scales proportionally to Komar energy. We then compute the heat capacity in both scenarios, discussing the black hole stability conditions and the possible appearance of second-order phase transitions. Finally, we extend our analysis to the black hole core, showing that in this sector entanglement energy serves as a valuable tool towards discriminating between singular and regular solutions.