Revisiting quantum black holes from effective loop quantum gravity

We systematically study a family of loop quantizations for the classical Kruskal spacetimes using the effective description motivated from loop quantum gravity for four generic parameters, $c_o,m,{\delta }_b$, and ${\delta }_c$, where the latter two denote the polymerization parameters that capture the underlying quantum geometry. We focus on the family where polymerization parameters are constant on dynamical trajectories and of which the Ashtekar-Olmedo-Singh (AOS) and Corichi-Singh (CS) models appear as special cases. We study general features of singularity resolution in all these models due to quantum gravity effects and analytically extend the solutions across the white hole (WH) and black hole (BH) horizons to the exterior. We find that the leading term in the asymptotic expansion of the Kretschmann scalar is $r^{-4}$. However, for AOS and CS models, black holes with masses greater than solar mass, the dominant term behaves as $r^{-6}$ for the size of the observable Universe and our analysis can be used to phenomenologically constrain the choice of parameters for other models. In addition, one can uniquely fix the parameter $c_o$ by requiring that the Hawking temperature at the BH horizon to the leading order be consistent with its classical value for a macroscopic BH. Assuming that the BH and WH masses are of the same order, we are able to identify a family of choices of ${\delta }_b$ and ${\delta }_c$ which share all the desired properties of the AOS model.