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

Understand

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.