标题： pp-波时空中的同余收敛 显示英文标题

标题： Congruence Convergence in pp-wave Spacetime

摘要： 我们主张，pp波的著名测地线完备性性质，在测地线被提取为沿着Brinkmann坐标集延伸时可以被忽略。 这个问题在更一般的共轭收敛背景下进行了研究，并且我们表明，该问题对于非测地线共轭会导致多种问题。 讨论主要基于零共轭膨胀，同时也提供了广义的Raychaudhuri方程。 显示英文摘要

摘要： 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.