Loop quantization of spherically symmetric midi-superspaces : the interior problem

TL;DR

This paper develops an exact loop quantum gravity model for the interior of black holes with spherical symmetry, showing that quantum effects replace singularities with bounces and providing insights into semi-classical evolution.

Contribution

It presents an exact solution to the quantum theory of spherically symmetric black hole interiors using loop quantum gravity, including a relational evolution framework.

Findings

Singularity replaced by a quantum bounce

Exact solvability in the connection representation

Quantum effects influence the bounce region size

Abstract

We continue the study of spherically symmetric vacuum space-times in loop quantum gravity by treating the interior of a black hole. We start from a midi-superspace approach, but a simple gauge fixing leads to a Kantowski--Sachs form for the variables. We show that one can solve the quantum theory exactly in the (periodic) connection representation, including the inner product. The evolution can be solved exactly by de-parameterizing the theory and can be easily interpreted as a semi-classical evolution plus quantum corrections. A relational evolution can also be introduced in a precise manner, suggesting what may happen in situations where it is not possible to de-parameterize. We show that the singularity is replaced by a bounce at which quantum effects are important and that the extent of the region at the bounce where one departs from classical general relativity depends on the initial data.