Dirac perturbations and thermodynamic corrections in a F (R)-corrected black hole

Abstract We study fermionic dynamics and thermodynamic properties of a static and spherically symmetric black hole solution in F (R) gravity, focusing on the role of higher-curvature corrections and quantum effects in the strong-field regime. The black hole geometry is described by a lapse function that includes Planck-scale inverse-power corrections while reducing smoothly to the Schwarzschild solution at large distances. Using the fermionic tunnelling formalism, we derive the Hawking temperature and show that higher-curvature terms modify the surface gravity without altering the semiclassical interpretation of radiation. Quantum-gravity effects are incorporated through the generalized uncertainty principle, leading to a suppression of the Hawking temperature governed by the deformation parameter and the fermion mass. We further analyze massless Dirac perturbations propagating on the corrected background. The associated effective potentials preserve a single-barrier structure, allowing the computation of quasinormal mode frequencies within the WKB approximation. Higher-curvature corrections introduce moderate quantitative shifts in the spectra while leaving their qualitative structure unchanged. In addition, we consider nonperturbative exponential corrections to the black hole entropy and examine their impact on the internal energy, Helmholtz free energy, effective pressure, and heat capacity. These corrections are negligible for large horizons but become relevant near the Planck scale, where they modify the thermodynamic response of the system.