Loop quantization of the Schwarzschild interior revisited

TL;DR

This paper revisits loop quantum gravity quantization of the Schwarzschild interior, proposing a new approach that yields a singularity-free bounce and a white-hole interior with a mass related to the original black hole.

Contribution

It introduces a novel, auxiliary-structure-independent loop quantization method for the Schwarzschild interior that ensures a correct low curvature limit and resolves the classical singularity.

Findings

Quantum constraint is well-defined past the singularity.

Effective dynamics show a bounce into an expanding regime.

White-hole mass scales with the cube of the black hole mass.

Abstract

The loop quantization of the Schwarzschild interior region, as described by a homogeneous anisotropic Kantowski-Sachs model, is re-examined. As several studies of different -inequivalent- loop quantizations have shown, to date there exists no fully satisfactory quantum theory for this model. This fact poses challenges to the validity of some scenarios to address the black hole information problem. Here we put forward a novel viewpoint to construct the quantum theory that builds from some of the models available in the literature. The final picture is a quantum theory that is both independent of any auxiliary structure and possesses a correct low curvature limit. It represents a subtle but non-trivial modification of the original prescription given by Ashtekar and Bojowald. It is shown that the quantum gravitational constraint is well defined past the singularity and that its effective dynamics possesses a bounce into an expanding regime. The classical singularity is avoided, and a semiclassical spacetime satisfying vacuum Einstein's equations is recovered on the "other side" of the bounce. We argue that such metric represents the interior region of a white-hole spacetime, but for which the corresponding "white-hole mass" differs from the original black hole mass. Furthermore, we find that the value of the white-hole mass is proportional to the third power of the starting black hole mass.