Dipolar particles in general relativity

Abstract

The dynamics of ‘dipolar particles’, i.e. particles endowed with a 4-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's worldline, and of the dipole moment vector, considered as a dynamical variable. The first part of the action is inspired by that of a particle with spin moving on an arbitrary gravitational background. The second part is intended to describe, at some effective level, the internal non-gravitational force linking together the ‘microscopic’ constituents of the dipole. We find that some solutions of the equations of motion and evolution of the dipolar particles correspond to an equilibrium state for the dipole moment in a gravitational field. Under some hypothesis we show that a fluid of dipolar particles, supposed to constitute the dark matter, reproduces the modified Newtonian dynamics (MOND) in the non-relativistic limit. We recover the main characteristics of a recently proposed quasi-Newtonian model of ‘gravitational polarization’.