The dynamics of "dipolar particles", i.e. particles endowed with a
four-vector mass dipole moment, is investigated using an action principle in
general relativity. The action is a specific functional of the particle's world
line, 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".Comment: 33 pages, 6 figures, to appear in Classical and Quantum Gravit
