Curved Spacetime Dirac Equation Revisited

Abstract

We revisit the Curved Spacetime (CST) Dirac equation that we presented earlier and our motive for this is to proffer a new alternative and elegant derivation of this equation. Having done this, we re-examine the resulting energy-momentum dispersion relation. It is seen that this energy-momentum dispersion relation is capable of describing massive braydons, luxons and tachyons. It is seen that how a particle turnouts to either be a braydon (k= 0), luxon (k=− 1) or a tachyon (k=+ 1) depends on the curvature (k= 0,±1) associated with the particle in question. The derived refractive index, nr, of a non-vacuo material medium predicts time-delays in the arrival times of cosmological photons of different frequencies emanating simultaneously from the same region of space as is the case with time-delays observed in radio photons emanating from GRB events. In its functional form, the derived formula for, nr, qualitatively fits the time-delays observed in GRBs and allows for the determination of the photon mass.