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

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.

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• Recovering a MOND-like acceleration law in mimetic gravity
• Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling
• Conservation laws in gravitational theories with general nonminimal coupling
• On the consistency of non-minimally coupled f(R) gravity
• Equations of motion in gravity theories with nonminimal coupling: a loophole to detect torsion macroscopically?
• On the dynamics of classical particle with spin
• The Raychaudhuri equation for spinning test particles