Snyder dynamics in a Schwarzschild spacetime

TL;DR

This paper investigates how Snyder's noncommutative geometry affects particle orbits in Schwarzschild spacetime, revealing modifications to perihelion shift and violations of the equivalence principle, thus constraining the model's parameters.

Contribution

It introduces the application of Snyder symplectic structure to Schwarzschild spacetime, showing its impact on orbital dynamics and fundamental principles.

Findings

Additional perihelion shift contribution

Violation of the equivalence principle

Constraints on Snyder model parameters

Abstract

We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.