Black holes in loop quantum gravity: the complete space-time

TL;DR

This paper presents an exact semi-classical solution in loop quantum gravity that removes the black hole singularity and suggests a global structure similar to a regular Reissner-Nordström spacetime with a Cauchy horizon.

Contribution

It provides a complete, exact solution for the quantum-corrected Schwarzschild spacetime in loop quantum gravity, extending previous partial or numerical results.

Findings

Singularity is eliminated in the quantum-corrected spacetime.

The global structure resembles a singularity-free Reissner-Nordström spacetime.

A Cauchy horizon appears in the quantum-corrected solution.

Abstract

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semi-classical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner--Nordstr\"om space-time including a Cauchy horizon is suggested.