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

► We study the effect of acceleration on the Dirac electron in the presence of an electromagnetic field, where the acceleration induces an electric field. ► Spin currents appear due to the total effective electric field via the total spin-orbit interaction. ► We derive the expression for the spin dependent force and the spin Hall current, which is zero for a particular acceleration. ► The role of the momentum space Berry curvature in an accelerating system is discussed. ► An expression for the spin polarization for time dependent acceleration is derived.