Non-geodesic motion in $f({\mathcal G})$ gravity with non-minimal coupling

TL;DR

This paper explores how non-minimal coupling in $f( ext{Gauss-Bonnet})$ gravity causes test particles to deviate from geodesic motion due to an extra force, affecting their relative accelerations.

Contribution

It demonstrates that in $f( ext{Gauss-Bonnet})$ gravity with non-minimal coupling, particles experience a new force leading to non-geodesic trajectories, a novel insight into modified gravity dynamics.

Findings

Particles experience an extra force normal to their four-velocity.

The form of the extra force depends on the specific $f( ext{Gauss-Bonnet})$ function.

The extra force influences the relative accelerations of particles.

Abstract

The dynamics of test particles in $f(\mathcal G)$ modified Gauss-Bonnet gravity is investigated. It is shown that in $f({\mathcal G})$ gravity models with non-minimal coupling to matter, particles experience an extra force normal to their four-velocities and as a result move along non- geodesic world-lines. The explicit form of the extra force depends on the function of the Gauss-Bonnet term included in coupling term. The effects of this force on the relative accelerations of particles are studied.