Fractional Corrections to Black Hole Spacetimes: Invariant Formulation, Quasinormal Modes, and Evaporation in Schwarzschild, Reissner-Nordström, and Kerr Geometries

We investigate the consequences of a fully invariant formulation of fractional gravity on classical black hole spacetimes. Starting from a fractional action in which the fractional parameter is promoted to a dynamical scalar field, we derive the exact Schwarzschild solution as the ground state of the theory, ensuring diffeomorphism invariance and the conservation of the energy–momentum tensor. Allowing the fractional parameter to vary spatially introduces controlled corrections to the metric, effectively modifying the black hole mass function and horizon structure. We compute analytic WKB approximations for quasinormal modes, highlighting shifts in both real and imaginary frequencies due to fractional corrections. Hawking temperature and entropy are correspondingly modified, yielding corrections to the black hole evaporation rate. We extend these results to charged Reissner–Nordström and rotating Kerr black holes, deriving analytic estimates for quasinormal modes, horizon shifts, and temperature corrections within the fractional framework. Our results demonstrate that fractional modifications provide a consistent, covariant generalization of classical black hole physics, offering a novel avenue for exploring semiclassical and phenomenological implications of fractional geometry.