Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures

TL;DR

This paper investigates particle motion in a Lorentz-violating bumblebee gravity background with Snyder noncommutative algebra, revealing modifications to perihelion shift and orbital periods, and discusses potential observational constraints.

Contribution

It introduces a combined framework of bumblebee gravity and Snyder noncommutative algebra to analyze classical particle orbits and their deviations from standard predictions.

Findings

Perihelion shift expression is generalized with two parameters.

Time period of revolution is affected by Lorentz violation, except for circular orbits.

Parameters can be constrained using existing observational methods.

Abstract

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.