Effective models of non-singular quantum black holes

TL;DR

This paper constructs and analyzes non-singular black hole models with quantum corrections at horizon scales, revealing thermodynamic phase transitions, observable signatures, and potential implications for the information paradox.

Contribution

It introduces a class of non-singular black hole solutions with a quantum scale parameter, extending previous models and exploring their thermodynamics and phenomenology.

Findings

Existence of black holes with a quantum scale parameter that can have two horizons or be horizonless.

Identification of a second-order phase transition near extremality when the quantum scale is comparable to the Schwarzschild radius.

Observable signatures in photon orbits and quasinormal modes indicating quantum effects at horizon scales.

Abstract

We investigate how the resolution of the singularity problem for the Schwarzschild BH could be related to the presence of quantum gravity effects at horizon scales. Motivated by the analogy with the cosmological Schwarzschild-dS solution, we construct a class of non-singular, static, asymptotically-flat BH solutions with a dS core, sourced by an anisotropic fluid, which encodes the quantum corrections. The latter are parametrized by a single length-scale $\ell$, which has a dual interpretation as an effective "quantum hair" and as the length-scale resolving the classical singularity. Depending on the value of $\ell$, 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 BH 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 $\ell$ is of order of the classical Schwarzschild radius $R_{\rm S}$. BHs with $\ell\sim R_{\rm S}$ are thermodynamically preferred with respect to those with $\ell\ll R_{\rm S}$, 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 AdS$_2\times$ S$^2$, signalizing the possible relevance of these models for the information paradox. We show that the presence of quantum corrections with $\ell\sim R_{\rm S}$ have observable phenomenological signatures in the photon orbits and in the QNMs spectrum. In particular, in the near-extremal regime, the imaginary part of the spectrum scales with the temperature as $c_1/\ell+c_2\ell T_\text{H}^2$, while it goes to zero linearly in the near-horizon limit. Our general findings are confirmed by revisiting two already-known models, namely the Hayward and gaussian-core BHs.