Coherent quantum hairy black holes from gravitational decoupling: regularity, geodesics, and scalar ringdown

Abstract

We construct a coherent-state quantum extension of gravitational-decoupling (GD) hairy black holes, in which the classical spacetime geometry emerges as the mean-field limit of a finite graviton condensate, while quantum fluctuations provide a natural short-distance regulator. The coherent quantum GD hairy black hole metric is obtained by Gaussian smearing of the gravitational potential, with an effective width encoding the size of the quantum core. The resulting geometry is free of curvature singularities over appropriate parameter ranges and exhibits a modified horizon structure. We also investigate geodesic motion in the coherent quantum GD hairy spacetime and find significant deviations from the classical Reissner-Nordström (RN) geometry. In particular, the photon ring, critical impact parameter, and light deflection are modified by the combined effects of quantum corrections and GD hair, providing potential strong-field tests of deviations from general relativity. Finally, we employ the WKB approximation to show that the coherent quantum GD hairy black hole has a quasinormal mode spectrum that differs from those of both the classical GD hairy and Schwarzschild black holes.

44 pages, 12 figures