Charged rotating quantum black holes

TL;DR

This paper explores the thermodynamics, phase transitions, and holographic properties of charged and rotating quantum black holes in a doubly holographic setup, revealing how charge and rotation influence critical behavior and quantum effects.

Contribution

It extends previous models by including charge and rotation, providing new insights into black hole thermodynamics, phase transitions, and quantum inequalities in a semi-classical holographic framework.

Findings

Charge and rotation eliminate re-entrant phase transitions.

Critical exponents differ from mean-field theory in neutral static cases.

Quantum effects are significant near the mass-gap energy scale.

Abstract

We investigate the thermodynamic and holographic properties of charged and rotating quantum black holes in a doubly holographic braneworld setup. These quantum black holes are derived from the anti-de Sitter C-metric and are exact solutions to a semi-classical gravitational theory which incorporates all orders of the backreaction of quantum fields on spacetime. The inclusion of both charge and rotation extends and generalizes previous studies. The thermodynamics and critical behavior of the black holes are examined from the bulk, brane, and boundary perspectives, and we demonstrate that the inclusion of either charge or rotation removes the re-entrant phase transitions seen in the neutral-static case. The critical exponents of the system are calculated using numerical methods and found to differ from the standard mean field theory values for the neutral-static black holes' re-entrant phase transitions, but in agreement with mean-field theory for the phase transitions of the black holes with charge and rotation. Additionally, to test the validity of the semiclassical treatment, we study a mass-gap energy scale $M_{\rm gap}$ to identify regimes where quantum fluctuations of spacetime geometry are expected to become significant and speculate about a connection with weak cosmic censorship gedankenexperiments. We also generalize the quantum Penrose inequality and the quantum reverse isoperimetric inequality to include charge and rotation. Finally, we compute a renormalized gyromagnetic ratio and analyze it in the limit of large backreaction.