  We discuss the behaviour of external fields that interact with a Dirac
neutral particle with a permanent electric dipole moment in order to achieve
relativistic bound states solutions in a noninertial frame and in the presence
of a topological defect spacetime. We show that the noninertial effects of the
Fermi-Walker reference frame induce a radial magnetic field even in the absence
of magnetic charges, which is influenced by the topology of the cosmic string
spacetime. We then discuss the conditions that the induced fields must satisfy
to yield the relativistic bound states corresponding to the
Landau-He-McKellar-Wilkens quantization in the cosmic string spacetime. Finally
we obtain the Dirac spinors for positive-energy solutions and the Gordon
decomposition of the Dirac probability current.
