Geodesic motion in Bogoslovsky-Finsler spacetimes
Résumé
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 with a homogeneous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaître model.
Mots clés
General relativity
alternative theories of gravity
gravitational radiation: plane wave
Einstein-Maxwell equation: solution
particle: massive
deformation
special relativity
general relativity
gravitation
background
transverse
structure
geodesic
Einstein
pp-wave
Finsler
family
space-time
curvature
group theory
Robertson-Walker
algebra: Lie
group: Lie