Homothetic congruences in general relativity

Abstract

The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy–momentum deposit of the chosen gravitational system. This is pursued through the inclusion of the base manifold’s cotangent bundle in a generalized Raychaudhuri equation and its kinematical expressions. Exploiting an electromagnetic energy–momentum tensor as the source of non-gravitational effects, I investigate the evolution of the mentioned homothetic congruences, as they fall onto a Reissner–Nordström black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles.