Non-singular naked solutions in quantum spacetime

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.