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Weak gravitational field in Finsler–Randers space and Raychaudhuri equation

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Abstract

The linearized form of the metric of a Finsler–Randers space is studied in relation to the equations of motion, the deviation of geodesics and the generalized Raychaudhuri equation are given for a weak gravitational field. This equation is also derived in the framework of a tangent bundle. By using Cartan or Berwald-like connections we get some types “gravito-electromagnetic” curvature. In addition we investigate the conditions under which a definite Lagrangian in a Randers space leads to Einstein field equations under the presence of electromagnetic field. Finally, some applications of the weak field in a generalized Finsler spacetime for gravitational waves are given.

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Acknowledgments

The author is grateful to the University of Athens (Special Accounts for Research Grants) for the support to this work.

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  1. Department of Mathematics, University of Athens, 15784 , Athens, Greece

    P. C. Stavrinos

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  1. P. C. Stavrinos
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Correspondence to P. C. Stavrinos.

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Stavrinos, P.C. Weak gravitational field in Finsler–Randers space and Raychaudhuri equation. Gen Relativ Gravit 44, 3029–3045 (2012). https://doi.org/10.1007/s10714-012-1438-0

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  • DOI: https://doi.org/10.1007/s10714-012-1438-0

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