On the Pure Axial Current of Lorentz Gauge Theory of Gravity.

When energies haven't reached the Planck scale, the source of Lorentz guage theory decomposes to a fully anti-symmetric and a remaining sector. While the latter generates the classical gravity, the former produces a field that only couples to the spin of fermions. At low energies the two fields can not be mixed under any transformation and represent two independent forces. Due to the universal nature of Lorentz transformations, the two gravitational fields have to interact with any fermion including those that constitute dark matter. Furthermore, the spin-generated gravity is very stronger than the classical one and is axial. Hence, it can be one of the long sought mediators, or the only one, between dark and baryonic matters. A model for dark matter is proposed consequently. The quantum expectation of the sources are derived and are used to find the equation of motion of particles. It is shown that not only bosons but also fermions will follow the geodesic motion if placed in a classical gravitational field. We report that the spin-generated gravity is an inverse square force between the spin of two fermions. A tabletop experimental test of the force is proposed.