  In this paper we study the quantum dynamics of a neutral particle in the
presence of a topological defect. We investigate the appearance of a geometric
phase in the relativistic quantum dynamics of neutral particle which possesses
permanent magnetic and electric dipole moments in the presence of an
electromagnetic fields in this curved background. The nonrelativistic quantum
dynamics are investigated using the Foldy-Wouthuysen expansion. The
gravitational Aharonov-Casher and He-Mckellar-Wilkens effects are investigated
for a series of electric and magnetic fields configurations.
