Charged regular black holes in quantum gravity: from thermodynamic stability to observational phenomena

Abstract

We investigate the thermodynamic, astrophysical, and observational properties of charged nonsingular black holes within the framework of quantum gravity and nonlinear electrodynamics. Our study focuses on the Frolov black hole model, which generalizes the Reissner-Nordstr & ouml;m and Hayward solutions through the inclusion of a cosmological-type parameter alpha.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha .$$\end{document} By employing the Gauss-Bonnet theorem (GBT), we derive the Hawking temperature and heat capacity, identifying phase transition points that govern black hole stability. We extend this analysis by incorporating generalized uncertainty principle corrections, revealing modifications to entropy and thermodynamic behavior. In the context of weak gravitational lensing, we compute the deflection angle using GBT and analyze its variations in vacuum and plasma media, emphasizing the role of charge and quantum effects on light propagation. Furthermore, we examine quasi-periodic oscillations by evaluating epicyclic frequencies in accretion disks, linking them to astrophysical observables. Lastly, we study the gravitational time delay of light signals, demonstrating how quantum-modified spacetime alters light propagation. Our results provide key insights into quantum-gravitational corrections to black hole physics, offering potential observational signatures relevant to gravitational wave studies, black hole imaging, and precision tests of strong-field gravity. Throughout this work, the term quantum gravity is used in an effective sense, referring to quantum aspects of black hole physics such as GUP-induced corrections, rather than to a complete and established quantum theory of gravitation.