Quantum space-time of a charged black hole

TL;DR

This paper applies loop quantum gravity techniques to quantize charged black holes, resolving classical singularities and suggesting quantum effects may stabilize Cauchy horizons, thus advancing understanding of quantum black hole structure.

Contribution

It introduces a new quantization of spherically symmetric electrovacuum gravity with an Abelianized constraint algebra, providing explicit solutions and demonstrating singularity resolution.

Findings

Quantum space-time resolves classical singularities inside charged black holes.

Explicit solutions of the physical Hilbert space are constructed.

Quantum effects may stabilize Cauchy horizons, pending further analysis.

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 space-times resolve the singularity present in the classical theory inside charged black holes and allows to extend the space-time through where the singularity used to be into new regions. We show that quantum discreteness of space-time may also play a role in stabilizing the Cauchy horizons, though back reaction calculations are needed to confirm this point.