Effective models of nonsingular quantum black holes

Abstract

We investigate how the resolution of the singularity problem for the Schwarzschild black hole could be related to the presence of quantum gravity effects at horizon scales. Motivated by the analogy with the cosmological Schwarzschild-de Sitter solution, we construct a broad class of nonsingular, static, asymptotically flat black-hole solutions with a de Sitter (dS) core, sourced by an anisotropic fluid, which effectively encodes the quantum corrections. The latter are parametrized by a single length-scale $\ensuremath{\ell}$, which has a dual interpretation as an effective ``quantum hair'' and as the length-scale resolving the classical singularity. Depending on the value of $\ensuremath{\ell}$, these solutions can have two horizons, be extremal (when the two horizons merge) or be horizonless exotic stars. We also investigate the thermodynamic behavior of our black-hole solutions and propose a generalization of the area law in order to account for their entropy. We find a second-order phase transition near extremality, when $\ensuremath{\ell}$ is of order of the classical Schwarzschild radius ${R}_{\mathrm{S}}$. Black holes with $\ensuremath{\ell}\ensuremath{\sim}{R}_{\mathrm{S}}$ are thermodynamically preferred with respect to those with $\ensuremath{\ell}\ensuremath{\ll}{R}_{\mathrm{S}}$, supporting the relevance of quantum corrections at horizon scales. We also find that the extremal configuration is a zero-temperature, zero-entropy state with its near-horizon geometry factorizing as ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{2}$, signalizing the possible relevance of these models for the information paradox. Finally, we show that the presence of quantum corrections with $\ensuremath{\ell}\ensuremath{\sim}{R}_{\mathrm{S}}$ have observable phenomenological signatures in the photon orbits and in the quasinormal modes (QNMs) spectrum. In particular, in the near-extremal regime, the imaginary part of the QNMs spectrum scales with the temperature as ${c}_{1}/\ensuremath{\ell}+{c}_{2}\ensuremath{\ell}{T}_{\mathrm{H}}^{2}$, while it goes to zero linearly in the near-horizon limit. Our general findings are confirmed by revisiting two already known models, which are particular cases of our general class of models, namely the Hayward and Gaussian-core black holes.