# Raychaudhuri equation with zero point length

## TL;DR

This paper explores how incorporating a zero-point length into the Raychaudhuri equation modifies spacetime geometry, potentially preventing singularities and capturing quantum gravity effects without relying on specific symmetries.

## Contribution

It introduces a generalized Raychaudhuri equation accounting for zero-point length, affecting geodesic congruence behavior in arbitrary spacetimes, and suggests implications for singularity avoidance.

## Key findings

- Zero-point length leads to non-zero cross-sectional area at coincidence limit.
- Modifies expansion and its rate, deviating from classical predictions.
- Potential to prevent caustic formation and singularities in quantum spacetime.

## Abstract

The Raychaudhuri equation for a geodesic congruence in the presence of a zero-point length has been investigated. This is directly related to the small-scale structure of spacetime and possibly captures some quantum gravity effects. The existence of such a minimum distance between spacetime events modifies the associated metric structure and hence the expansion as well as its rate of change deviates from standard expectations. This holds true for any kind of geodesic congruences, including time-like and null geodesics. Interestingly, this construction works with generic spacetime geometry without any need of invoking any particular symmetry. In particular, inclusion of a zero-point length results into a non-vanishing cross-sectional area for the geodesic congruences even in the coincidence limit, thus avoiding formation of caustics. This will have implications for both time-like and null geodesic congruences, which may lead to avoidance of singularity formation in the quantum spacetime.