Non-singular naked solutions in quantum spacetime

TL;DR

This paper explores non-singular quantum black hole models using polymer quantization, revealing mass-dependent transition surfaces, Planck-scale remnants, and unique charged solutions without horizons for certain mass ranges.

Contribution

It extends previous models to include solutions with smaller masses, identifying charged, horizonless states and analyzing their properties within quantum spacetime.

Findings

Existence of minimal radius without horizons for certain masses

Charged solutions are only possible in the lower mass range

Hawking evaporation leads to Planck-sized remnants

Abstract

Polymer models have been used to describe non-singular quantum black holes, where the classical singularity is replaced by a transition from a black hole to a white hole. In a previous letter, in the context of a uni-parametric model with asymptotic flat exterior metric, we fixed the radius of the transition surface through the identification of its area with the area gap of Loop Quantum Gravity. This revealed a dependence of the polymerisation parameter on the black hole mass, where the former increases as the latter decreases, and it also enabled the extension of the model to Planck-scale black holes. We have identified the existence of limiting states with masses $m \geq \sqrt{2}/4$ and zero surface gravity, showing that Hawking evaporation asymptotically leads to remnant black holes of Planck size. In the present paper we consider solutions with $m < \sqrt{2}/4$, observing again the presence of a minimal radius, but without formation of horizons. Diversely from the previous mass range, only charged solutions are allowed in this case.