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

TL;DR

This work studies a covariant quantum-corrected Reissner-Nordström black hole with parameters $M$, $Q$, and the quantum correction $\zeta$ to identify observable imprints in strong gravity. The authors analyze neutral-particle dynamics to derive fundamental frequencies and apply several QPO models, performing Bayesian MCMC inference with data from multiple black-hole candidates to constrain the spacetime parameters. They further examine massless scalar perturbations via a Schrödinger-like equation, compute greybody factors, and evaluate the high-frequency energy emission, showing that $\zeta$ modulates both the potential barrier and the Hawking spectrum. Finally, they assess thermal fluctuations, obtaining logarithmic entropy corrections that become relevant only for small horizons, and conclude that $\zeta$ leaves detectable signatures across dynamical and thermodynamical properties, enabling observational constraints on quantum-gravity effects. Future work could extend the analysis to quasinormal modes and rotating quantum-corrected black holes to sharpen observational tests.

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.

Figures (15)

• Figure 1: Behavior of the effective potential $U_{\rm eff}$ as a function of dimensionless radial distance $r/M$ for different values of quantum correction parameter $\zeta$. Here $Q/M=1$.
• Figure 2: Behavior of the squared specific angular momentum per unit mass and squared specific energy of test particles as functions of the dimensionless radial coordinate $r/M$ for various values of the quantum correction parameter $\zeta$. Here $Q/M=1$.
• Figure 3: The ISCO radius $r_{\rm ISCO}/M$ given in Eq. (\ref{['rISCO_final']}) of quantum-corrected RN BH for various values of the quantum parameter $\zeta/M$ and charge $Q/M$.
• Figure 4: Behavior of the mass times the effective force $M\,\mathcal{F}$ as a function of dimensionless radial distance $r/M$ by varying quantum correction parameter.
• Figure 5: Representative examples of the radial profiles of the observational frequencies $\nu_i$ for different values of the BH parameters.