Congruence Convergence in pp-wave Spacetime

Abstract

We argue that the well-known geodesic completeness property of pp-waves, can be disregarded once the geodesics are extracted as being extended along sets of Brinkmann coordinates. This issue is investigated in the more general context of congruence convergence and we show that the problem leads to diverse issues for non-geodesic congruences. The discussion is mostly based on the null congruence expansion and a generalized Raychaudhuri equation is also provided.