Loop quantization of the Schwarzschild black hole

TL;DR

This paper applies loop quantum gravity techniques to the Schwarzschild black hole, successfully resolving the classical singularity and introducing new quantum observables related to spin network states.

Contribution

It develops a gauge-independent loop quantization of Schwarzschild black holes, explicitly constructs solutions, and reveals quantum observables absent in classical theory.

Findings

Singularity inside black holes is resolved in the quantum model.

New quantum observables related to spin networks emerge.

The algebra of constraints becomes Abelian, simplifying quantization.

Abstract

We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra. This allows the completion of the Dirac quantization procedure using loop quantum gravity techniques. We can construct explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. New observables living in the bulk appear at the quantum level (analogous to spin in quantum mechanics) that are not present at the classical level and are associated with the discrete nature of the spin network states of loop quantum gravity. The resulting quantum space-times resolve the singularity present in the classical theory inside black holes.