Fermionic perturbations and spinning particle dynamics in asymptotically safe charged black holes

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Abstract

We investigate a quantum-corrected charged black hole obtained by promoting the Newtonian coupling to a scale-dependent quantity, as motivated by renormalization group improvement in Quantum Einstein Gravity. This yields a modified Reissner-Nordstrm spacetime where quantum effects are encoded through radial running of the gravitational coupling, while the classical limit is recovered at large distances. Fermionic Hawking radiation is studied within a tunneling framework based on a Generalized Uncertainty Principle-deformed Dirac equation. The resulting Hawking temperature is reduced relative to the semiclassical case, reflecting minimal-length effects that propagate into the thermodynamic sector. We derive quantum-corrected internal energy, Helmholtz free energy, and pressure within the extended phase space formalism. Deviations from classical thermodynamics are most pronounced near the event horizon and become negligible in the weak-field regime. The dynamical response is examined through fermionic perturbations by constructing the effective potential and employing a semiclassical approximation to compute the quasinormal mode spectrum and quality factors. Results indicate that running gravitational coupling mainly affects damping properties with milder impact on oscillation frequencies. Tidal forces analyzed via the geodesic deviation equation reveal characteristic transition radii where the nature of tidal deformation changes due to quantum corrections. Finally, motion of spinning magnetized test particles is explored through an effective radial potential, showing that quantum corrections primarily modify dynamics in the strong-field region while leaving asymptotic behavior essentially classical. Our results demonstrate how scale-dependent gravity and minimal-length effects jointly modify both thermodynamic and dynamical properties of charged black holes.

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