Some phenomenological aspects of a quantum-corrected Reissner-Nordström black hole: quasi-periodic oscillations, scalar perturbations and thermal fluctuations

Abstract: In this work, we investigate several phenomenological aspects of a covariant quantum-corrected Reissner-Nordström black hole characterized by the mass $M$, electric charge $Q$, and the quantum correction parameter $ζ$. We first study the motion of neutral test particles and derive the fundamental orbital and epicyclic frequencies, which are then employed to analyze different quasi-periodic oscillation (QPO) models. Using observational QPO data from stellar-mass, intermediate-mass, and supermassive black hole candidates, we perform a Bayesian parameter estimation through a Markov Chain Monte Carlo (MCMC) analysis and obtain constraints on the black hole parameters. The results show that the presence of the quantum correction significantly affects the location of the QPO radii and the separation between the QPO orbit and the ISCO. We then examine the scalar perturbations by deriving the Schrödinger-like radial equation and the corresponding effective potential. The influence of the parameters $Q$ and $ζ$ on the perturbation potential and stability of the spacetime is discussed. Furthermore, we compute the greybody factor and the energy emission rate in the high-frequency (geometric-optics) regime, showing how the quantum correction modifies the absorption probability and radiation spectrum. Finally, we study the effect of thermal fluctuations on the black hole entropy and obtain the logarithmic corrections to the Bekenstein-Hawking area law. We show that these corrections become important for small black holes, while for large horizon radius the standard thermodynamic behavior is recovered. Our analysis demonstrates that the quantum correction parameter leaves observable imprints on both dynamical and thermodynamical properties of the spacetime and can be constrained through QPO observations.