Spectral Dimensionality of Spacetime Around a Radiating Schwarzschild Black-Hole

In this work we study the spectral dimensionality of spacetime around a radiating Schwarzschild black hole using a recently introduced formalism of quantum gravity, where the alterations of the gravitational field produced by the radiation are represented on an extended manifold, and describe a non-commutative and nonlinear quantum algebra. The relation between classical and quantum perturbations of spacetime can be measured by the parameter z≥0. In this work we have found that when z=(1+3)/2≃1.3660, a relativistic observer approaching the Schwarzschild horizon perceives a spectral dimension N(z)=4θ(z)−1≃2.8849, which is related to quantum gravitational interference effects in the environment of the black hole. Under these conditions, all studied Schwarzschild black holes with masses ranging from the Planck mass to 1046 times the Planck mass present the same stability configuration, which suggests the existence of a universal property of these objects under those particular conditions. The difference from the spectral dimension previously obtained at cosmological scales leads to the conclusion that the spacetime dimensionality is scale-dependent. Another important result presented here is the fundamental alteration of the effective gravitational potential near the horizon due to Hawking radiation. This quantum phenomenon prevents the potential from diverging to negative infinity as the observer approaches the Schwarzschild horizon.