Raychaudhuri equation in spacetimes with torsion

Abstract

Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent and orthogonal effects on the congruence; in particular, the presence of a completely generic torsion field contributes to a relative acceleration between test particles. We derive, for the first time in the literature, the Raychaudhuri equation for a congruence of timelike and null curves in a spacetime with the most generic torsion field.The Authors wish to thank José P. S. Lemos for early discussions on a first version of the paper. We thank FCT-Portugal for financial support through Project No. PEst-OE/FIS/UI0099/2015. PL thanks IDPASC and FCT-Portugal for financial support through Grant No. PD/BD/114074/2015. VV is supported by the FCTPortugal grant SFRH/BPD/77678/2011.info:eu-repo/semantics/publishedVersio

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This paper was published in Universidade do Minho: RepositoriUM.

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