Test particle motion in modified gravity theories

TL;DR

This paper derives generalized equations of motion for test particles in modified gravity theories where energy-momentum is not conserved, extending the Mathisson-Papapetrou equations to include spinning particles.

Contribution

It introduces a generalized form of the equations of motion for test particles in modified gravity, including spinning particles, where the energy-momentum tensor's divergence is non-zero.

Findings

Derived generalized equations of motion for neutral test particles.

Extended Mathisson-Papapetrou equations to modified gravity contexts.

Analyzed motion of spinning particles in modified gravity theories.

Abstract

We derive the equations of motion of an electrically neutral test particle for modified gravity theories in which the covariant divergence of the ordinary matter energy-momentum tensor dose not vanish (i.e. $\nabla_{\mu}T^{\mu\nu}\neq0$). In fact, we generalize the Mathisson-Papapetrou equations by deriving a general form for the equations of motion of a test particle. Furthermore, using the generalized Mathisson-Papapetrou equations, we investigate the equations of motion of a pole-dipole (spinning) particle in the context of Modified Gravity (MOG).