  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.
