Black hole solutions in quantum phenomenological gravitational dynamics

We investigate black hole solutions in a modified gravity theory inspired by a phenomenological approach to quantum gravity based on spacetime thermodynamics developed by Alonso-Serrano and Li\ifmmode \check{s}\else \v{s}\fi{}ka. The field equations are traceless, similar 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.