Timelike geodesic vector field
= Timelike geodesic vector field
A timelike geodesic vector field is a smooth unit timelike field $u^a$ whose integral curves obey $u^b\nabla_bu^a=0$. Its <expansion scalar>, <shear tensor of a timelike congruence>, and <vorticity tensor of a timelike congruence> evolve according to the timelike <Raychaudhuri equation>.