Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

TL;DR

This paper derives quantum gravity corrections to the Raychaudhuri equation within loop quantum gravity, demonstrating that these modifications cause geodesic defocusing, prevent conjugate points, and resolve the classical black hole singularity.

Contribution

It introduces a modified Raychaudhuri equation incorporating loop quantum gravity effects, providing a mechanism for singularity resolution in black holes.

Findings

Quantum corrections cause geodesic defocusing.

Classical singularity is resolved in the effective theory.

Singularity theorems become inapplicable due to repulsive terms.

Abstract

We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.