Geodesic motion in Bogoslovsky-Finsler Spacetimes

Abstract

We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model.

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Cited by in corpus (14)

• Mathematical foundations for field theories on Finsler spacetimes
• Schwarzschild-like solutions in Finsler-Randers gravity
• On the non metrizability of Berwald Finsler spacetimes
• Applications of the Schwarzschild-Finsler-Randers model
• Randers pp-waves
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• Hidden symmetries from distortions of the conformal structure
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