Horizon entanglement area law from regular black hole thermodynamics

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.

14 pages, 7 figures

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• Quantum entanglement in cosmology
• Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes
• Topological regular black holes without Cauchy horizon
• Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models
• Imprints of screened dark energy on nonlocal quantum correlations
• The quantum relative entropy of the Schwarzschild black-hole and the area law
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• The area and volume laws for entanglement of scalar fields in flat and cosmological spacetimes