Quantization of Reissner-Nordstr\"{o}m Black Holes and Their Non-Singular Quantum Behavior

TL;DR

This paper applies loop quantum gravity techniques to Reissner-Nordström black holes, demonstrating that quantum effects can resolve classical singularities and lead to non-singular, well-behaved black hole models.

Contribution

It develops a loop quantum gravity framework for charged black holes, showing singularity avoidance through bounded operators and non-singular quantum evolution.

Findings

Scalar curvature diverging factor has a bounded spectrum

Quantum evolution remains non-singular

Singularity is avoided in symmetry-reduced models

Abstract

Quantization of different regions of the Reissner-Nordstr\"{o}m space time (charged black hole) is done in the framework of loop quantum gravity. The geometry of Reissner-Nordstr\"{o}m space-time is expressed in terms of Ashtekar variables which form the classical phase space of such a black hole. Using the loop quantization of phase space, the issue of singularity avoidance of such a black hole is addressed; based on spherically symmetry reduced models of loop quantum gravity, the operator analogue of the diverging factor of scalar curvature of the charged black hole is constructed and is shown to exhibit an upper bounded spectrum. This local criterion, together with the global one (non-singular quantum evolution equation) proves the avoidance of charged black hole singularity in symmetry reduced models of loop quantum gravity.