  This paper explores the relativistic behavior of spin--half particles
possessing an Electric Dipole Moment (EDM) in a curved spacetime background
induced by a spiral dislocation. A thorough review of the mathematical
formulation of the Dirac spinor in the framework of quantum field theory sets
the foundation for our investigation. By deriving the action that governs the
interaction between the spinor field, the background spacetime, and an external
electric field, we establish a framework to study the dynamics of the system.
Solving the resulting wave equation reveals a set of coupled equations for the
radial components of the Dirac spinor, which give rise to a modified energy
spectrum attributed to the EDM. To validate our findings, we apply them to the
geometric phase and thermodynamics.
