Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures

A metric with a Lorentz violating parameter is associated with the bumblebee gravity model. We study the motion of a particle in this bumblebee background where the dynamical variables satisfy non-canonical Snyder algebra along with some critical survey on the classical observations in the bumblebee background to see how these would likely differ from Schwarzschild background. It has been found that the perihelion shift acquires a generalized expression with two independent parameters. One of these two is connected with the Lorentz violating factor and the other is involved in the Snyder algebraic formulation. We also observe that the time period of revolution, in general, acquires a Lorentz violating factor in the bumblebee background, however, for the circular orbit, it remains unchanged even in the presence of the Lorentz violating factor in the bumblebee background. The parameters used here can be constrained with the same type of conjecture used earlier.

Automated summary

This study focuses on the metric and particle motion in the bumblebee gravity model, finding that the perihelion shift obtains a generalized expression in this model, and the revolution period is affected by a Lorentz violating factor in general. The parameters used can be constrained with a similar conjecture as before.