Effective models of non-singular 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 non-singular, 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 , which has a dual interpretation as an effective "quantum hair" and as the length-scale resolving the classical singularity. Depending on the value of , 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 is of order of the classical Schwarzschild radius RS. Black holes with ∼ RS are thermodynamically preferred with respect to those with RS, 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 AdS2× S 2 , signalizing the possible relevance of these models for the information paradox. Finally, we show that the presence of quantum corrections with ∼ RS have observable phenomenological signatures in the photon orbits and in the quasi-normal modes (QNMs) spectrum. In particular, in the near-extremal regime, the imaginary part of the QNMs spectrum scales with the temperature as c1/ + c2 T 2 H , 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.

Some Remarks on Non-Singular Spherically Symmetric Space-Times

“…The resulting solution is a non-vacuum solution of Einstein's equations. Explicit examples have been provided by Bardeen, Hayward and many others (for a partial list see [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] and references therein). Other related results can be found in [55][56][57].…”

Constraints on singularity resolution by nonlinear electrodynamics

“…This, again, leads to a contradiction, as the right hand side is manifestly unbounded as r → 0, whereas the left hand side should be bounded according to Eq. (35).…”

“…Indeed, electrically charged regular black holes constructed in [26][27][28] violate Maxwellian limit, while magnetically charged regular black holes in [29][30][31][32] do not. Dymnikova [33] showed that by relaxing Bronnikov's conditions (precisely, discarding Maxwellian limit), it is possible to obtain regular electrically charged black hole solution with so-called "de Sitter core", de Sitter behaviour as r → 0 (see also [34,35]). Another evision of the Bronnikov's no-go theorem was proposed in [36], based on a specific construction with core simulating a phase transition.…”