Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling

TL;DR

This paper derives covariant equations of motion for test bodies in a broad class of gravitational theories with nonminimal coupling, extending previous results and including spinning bodies via Synge's technique.

Contribution

It provides a general covariant derivation of equations of motion in theories with nonminimal coupling, including spinning bodies, and compares them to general relativity.

Findings

Generalized equations of motion for nonminimal coupling theories

Explicit equations for spinning test bodies

Comparison with general relativistic equations

Abstract

We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge's expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.