2025/05/05 by Mauricio Bellini, Juan Ignacio Musmarra, Bellini, Mauricio +5
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.2505.03011
openalex publication_date 2025/05/05 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
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 non-linear algebra. The ration between classical and quantum perturbations of spacetime can be measured by the parameter z ≥ 0. When z=(1+√(3))/2≃ 1.3660, a relativistic observer approaching the Schwarzschild horizon perceives a spectral dimension N(z)=4[θ(z)-1]≃ 2.8849. 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 an 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 dimensionality of spacetime 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 observable approaches the Schwarzschild horizon.