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

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.

Automated summary

This study examines the loop quantum gravity corrections to the Raychaudhuri equation inside a Schwarzschild black hole and near the classical singularity. It shows that the resulting effective equation leads to geodesic defocusing due to the appearance of repulsive terms, preventing the formation of conjugate points, making singularity theorems inapplicable, and ultimately resolving the singularity in this spacetime.