Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

TL;DR

This paper investigates how loop quantum gravity can prevent singularities in charged black holes by quantizing their interior and showing that curvature scalars become bounded, indicating singularity avoidance.

Contribution

It extends loop quantum gravity techniques to charged black holes, demonstrating bounded curvature operators and singularity resolution in Reissner-Nordström black holes.

Findings

Curvature scalar components are bounded in the quantum model.

Bound on curvature reduces to Schwarzschild case as charge Q approaches zero.

Quantum geometry suggests a mechanism for singularity avoidance.

Abstract

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordstr\"{o}m black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case $M^2> Q^2$. This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Swcharzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit $Q \rightarrow 0$. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.