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We have studied the spin dependent force and the associated momentum spaceBerry curvature in an accelerating system. The results are derived by takinginto consideration the non relativistic limit of a generally covariant Diracequation under the presence of electromagnetic field where the methodology ofFoldy-Wouthuysen transformation is applied to achieve the non relativisticlimit. Spin currents appear due to the combined action of the external electricfield, crystal field and the induced inertial electric field via the totaleffective spin-orbit interaction. In an accelerating frame, the crucial role ofmomentum space Berry curvature in the spin dynamics has also been addressedfrom the perspective of spin Hall conductivity. For time dependentacceleration, the expression for the spin polarization has been derived.

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature