On the loop quantization of an interior black hole model*

In this talk we present some recent investigations on the quantum theory underlying a recent extension of Kruskal spacetime, proposed by Ashtekar, Olmedo and Singh in the context of effective loop quantum cosmology. To this aim, we first introduce a Hamiltonian description of the interior region that is consistent with the effective dynamics. In such description, the spacetime geometry is described in terms of the typical holonomy-flux algebra employed in loop quantum cosmology, thus providing the starting point for the quantization of the black hole interior. We then develop the first steps to construct this quantum theory. In particular, we propose specific operators for the constraints of the system and, under reasonable assumptions, we deduce the formal expression of the physical states as functions of the black hole mass. These results pave the road for future investigations that aim to include genuine loop quantum effects on black hole spacetimes and their perturbations.