Coherent quantum hairy black holes from gravitational decoupling

Abstract

A quantum description of hairy black holes within gravitational decoupling (GD) is developed using coherent graviton states. Classical geometry emerges as the mean-field limit of a finite graviton condensate, while quantum fluctuations introduce a short-distance regulator. We construct a coherent quantum GD hairy black hole metric by Gaussian smearing the gravitational potential, with an effective width that encodes the size of the quantum core. The resulting geometry is free of curvature singularities over appropriate parameter ranges and exhibits modified horizon structures. The effective stress-energy tensor is derived, the energy conditions are analyzed, and the Misner-Sharp mass is computed. We investigate geodesics in the coherent quantum GD hairy black hole geometry, with relevant deviations from the RN case. Photon rings, critical impact parameters, and light deflection exhibit measurable strong-field modifications, allowing observational constraints on deviations from general relativity.

Figures (9)

• Figure 1: Metric function (left) and potential function (right) for the coherent quantum GD hairy black hole, with $R_{\rm s}/R_{\rm M} = 0.05$ and $R_{\rm Q}/R_{\rm M} = 0.1$.
• Figure 2: Metric function (left) and potential function (right) for the coherent quantum GD hairy black hole, with $R_{\rm s}/R_{\rm M} = 0.5$ and $R_{\rm Q}/R_{\rm M} = 0.4$.
• Figure 3: Metric function $f(r, \alpha)$ for different values of the ratios $R_{\rm s}/R_{\rm M}$ and $R_{\rm Q}/R_{\rm M}$.
• Figure 4: Normalized effective energy density (left) and normalized tangential pressure (right) for $R_{\rm s}/R_{\rm M} = 0.3$, $R_{\rm Q}/R_{\rm M} = 0.1$ and $\ell = M/e^2$.
• Figure 5: Behavior of the normalized mass function $m(r)/M$ for fixed $R_{\rm s}/R_{\rm M}=0.1$ and $R_{\rm Q}/R_{\rm M} = 0.1$ (left) and $R_{\rm Q}/R_{\rm M}=0.3$ (right).