Snyder Like Modified Gravity in Newton's Spacetime

TL;DR

This paper explores a geodesic interpretation of a Snyder-like deformed Kepler problem within a Newtonian spacetime framework, revealing curvature effects and conserved quantities influenced by deformation parameters.

Contribution

It introduces a novel approach to interpret Snyder-like deformations as geodesics in a Newtonian spacetime with a torsion-free connection, linking algebraic deformation to geometric curvature.

Findings

Curvature terms depend on mass and fundamental length, but are velocity independent.

Deformation modifies integrals of motion in the Kepler problem.

Geodesic interpretation provides insight into the effects of algebraic deformation.

Abstract

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity independent. In this sense, the effect of introducing a deformed algebra is examinated and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.