Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

TL;DR

This paper investigates how generalized uncertainty principle (GUP) modifications affect the Raychaudhuri equation inside Schwarzschild black holes, showing that some models can resolve singularities while others cannot.

Contribution

It computes GUP-inspired corrections to the Raychaudhuri equation in black hole interiors and analyzes four models, identifying which can resolve singularities.

Findings

Two GUP models lead to finite curvature and resolve singularities.

Two other models retain singularities despite GUP modifications.

GUP-dependent modifications influence the effective dynamics significantly.

Abstract

The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.