Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures

Abstract

A metric with a Lorentz violating parameter is associated with thebumblebee gravity model. We study the motion of a particle in thisbumblebee background where the dynamical variables satisfynon-canonical Snyder algebra along with some critical survey onthe classical observations in the bumblebee background to see howthese would likely differ from Schwarzschild background. It hasbeen found that the perihelion shift acquires a generalizedexpression with two independent parameters. One of these two isconnected with the Lorentz violating factor and the other isinvolved in the Snyder algebraic formulation. We also observe thatthe time period of revolution, in general, acquires a Lorentzviolating factor in the bumblebee background, however, for thecircular orbit, it remains unchanged even in the presence of theLorentz violating factor in the bumblebee background. Theparameters used here can be constrained with the same type ofconjecture used earlier.