Quantum spacetime of a charged black hole

Abstract

We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie algebra. We complete the Dirac quantization procedure using loop quantum gravity techniques. We present explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. The resulting quantum spacetimes resolve the singularity present in the classical theory inside charged black holes and allows us to extend the spacetime through where the singularity used to be into new regions. We argue that quantum discreteness of spacetime may also play a role in stabilizing the Cauchy horizons, though backreaction calculations are needed to confirm this point.