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We demonstrate, by analogy with electromagnetism, that the geometric contentin the theory of gravity is an indirect consequence of the fact that the gaugegroup in question is the Lorentz group SO(1,3). We hence construct fieldequations for gravity and a spin-1/2 particle in a gravitational field based ongauge considerations. Furthermore, we derive the weak field and Schroedingerlimits of the Dirac equation of the particle in the gravitational field,especially in Fermi normal coordinates and on the equatorial plane of the Kerrgeometry, following which we identify the terms to which the electromagneticpotentials A and Phi are analogous.

Gauging gravity with SO(1,3) for spin-1/2 particles