Remnant loop quantum black holes

Abstract

Polymer models inspired by Loop Quantum Gravity (LQG) have been used to describe non-singular quantum black holes with spherical symmetry, with the classical singularity replaced by a transition from a black hole to a white hole. A recent model, with a single polymerisation parameter, leads to a symmetric transition with same mass for the black and white phases, and to an asymptotically flat exterior metric. The radius of the transition surface is, however, not fixed, increasing with the mass. Following similar procedures, in a previous paper we have fixed that radius by identifying the minimal area on the transition surface with the area gap of LQG. This allowed to find a dependence of the polymerisation parameter on the black hole mass, with the former increasing as the latter decreases. It also permitted to extend the model to Planck scale black holes, with quantum fluctuations remaining small at the horizon. In the present paper we extend this analysis to charged black holes, showing that the Cauchy horizon lies beyond of the transition surface. We also show the existence of limiting states with zero surface gravity, the lightest one with $Q = 0$ and $m = \sqrt{2}/4$, and the heaviest with $Q = m = \sqrt{2}/2$. Using our solutions to approximate quasi-steady horizons, we show that Hawking evaporation leads asymptotically to these extremal states, leaving remnant black holes of Planck size.