Unified geometrical basis for the generalized Ehlers identities and Raychaudhuri equations

Abstract

It is shown that the timelike, spacelike and null versions of the Ehlers identity, as well as ensuing Raychaudhuri equations, might be all derived within a single geometrical approach based on the definition of the Riemann curvature tensor specified with respect to the corresponding congruence. Still, spacelike and null cases have a number of non-trivial peculiarities deserving special attention.