Consistency in the Quantum-Improved Charged Black Holes

TL;DR

This paper explores the thermodynamic and gravitational consistency of quantum-improved charged black holes with scale-dependent couplings, revealing conditions for their coherence and implications for early universe cosmology.

Contribution

It analyzes the consistency conditions at the thermodynamic and gravitational levels for quantum-improved charged black holes, including the role of scale-dependent couplings and quantum energy-momentum tensors.

Findings

Thermodynamic consistency allows arbitrary radial dependence of couplings.

Identifies a subtlety in the chemical potential with scale-dependent electromagnetic coupling.

Quantum modifications can drive isotropization in early universe cosmology.

Abstract

We investigate the consistency in the thermodynamics and the approaches at the equation and action levels for the quantum-improved charged black holes with scale-dependent couplings. For the quantum-improved Reissner-Nordstr\"om black holes, we find that the thermodynamic consistency allows both the Newton and electromagnetic couplings to have arbitrary dependence on the radial coordinate. We point out a subtlety in the chemical potential with the scale-dependent electromagnetic coupling in the study of thermodynamics. We also examine the compatibility of the Einstein equations at the equation and action levels with the Bianchi identity, identifying the need for an additional quantum energy-momentum tensor. We then find that the consistency between the approaches at the equation and action levels requires that the Newton coupling satisfy certain property. Finally, we extend the analysis to cosmological solutions, suggesting that quantum-induced modifications can drive the isotropization of the early universe.