TL;DR
This paper explores the behavior of homothetic congruences in general relativity, analyzing their evolution near a Reissner-Nordstrom black hole using a generalized Raychaudhuri equation and electromagnetic energy-momentum effects.
Contribution
It introduces a generalized Raychaudhuri equation incorporating the cotangent bundle to study homothetic congruences in gravitational fields with electromagnetic effects.
Findings
Homothetic congruences exhibit unique evolution patterns near black holes.
Electromagnetic effects significantly influence the kinematics of infalling congruences.
Results differ from traditional expectations for massive particle infall.
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-Nordstrom black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles.
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