Motion of pole-dipole and quadrupole particles in non-minimally coupled theories of gravity

TL;DR

This paper investigates how non-minimal coupling in gravity theories affects the motion of particles with pole-dipole and quadrupole moments, revealing that curvature-dependent functions induce quadrupole moments and modify particle trajectories.

Contribution

It derives the general equations of motion for polarized media with multipole moments in non-minimally coupled gravity theories, including specific cases involving curvature scalar, Riemann tensor, and Gauss-Bonnet invariant.

Findings

Induced quadrupole moments arise from curvature-dependent couplings.

Extra forces on particles can be expressed via induced moments.

Explicit equations of motion are provided for various coupling functions.

Abstract

We study theories of gravity with non-minimal coupling between polarized media with pole-dipole and quadrupole moments and an arbitrary function of the space-time curvature scalar $R$ and the squares of the Ricci and Riemann curvature tensors. We obtain the general form of the equation of motion and show that an induced quadrupole moment emerges as a result of the curvature tensor dependence of the function coupled to the matter. We derive the explicit forms of the equations of motion in the particular cases of coupling to a function of the curvature scalar alone, coupling to an arbitrary function of the square of the Riemann curvature tensor, and coupling to an arbitrary function of the Gauss-Bonnet invariant. We show that in these cases the extra force resulting from the non-minimal coupling can be expressed in terms of the induced moments.