Black hole solutions in quantum phenomenological gravitational dynamics

TL;DR

This work analyzes black hole solutions in a quantum phenomenological gravitational dynamics with traceless field equations and quadratic curvature terms. The static, vacuum, spherically symmetric sector splits into Branch I, which yields Schwarzschild-(A)dS with an integration-constant cosmological term, and Branch II, which produces horizonless geometries with spatial sections of constant curvature at the Planck scale. Linear perturbations on Branch I reproduce unimodular/GR behavior, while Branch II perturbations reduce to standard Regge-Wheeler/polar structures but with background-curvature–driven modifications and no new dynamical degrees of freedom. Overall, the theory yields GR-like black holes or exotic horizonless spacetimes in vacuum, with singularity resolution not realized in this setting; extending the analysis to matter fields or less symmetric configurations is needed to assess broader quantum-gravity implications.

Abstract

We investigate black hole solutions within a phenomenological approach to quantum gravity based on spacetime thermodynamics developed by Alonso-Serrano and Liška. The field equations are traceless, similarly to unimodular gravity, and include quadratic curvature corrections. We find that static, spherically symmetric, vacuum spacetimes in this theory split into two branches. The first branch is indistinguishable from corresponding solutions in unimodular gravity and describes Schwarzschild-(Anti) de Sitter black holes. The second branch instead describes horizonless solutions and is characterized by large values of the spatial curvature. We analyze the dynamics of first-order metric perturbations on both branches, showing that there are no deviations from unimodular gravity at this level.