Unifying Gravity and EM in Detail

Unify gravity and EM with the simplest asymmetric field strength tensor: \[S_{GEM}=\int\sqrt{-g}d^4 x(-(J_q^{\nu}-J_m^{\nu}) A_{\nu}-\frac{1}{4c^2}\nabla^{\mu}A^{\nu}\nabla_{\mu}A_{\nu})\] Particles with equal charges but different masses move differently, so mass charge breaks EM gauge symmetry. The field equations arise by varying the action with respect to the 4-potential, the metric is fixed up to a diffeomorphism. \[J_q^{\nu}-J_m^{\nu}=\nabla_{\mu}\nabla^{\mu}A^{\nu}\] With a constant potential, the exponential Rosen metric solves the field equations consistent with current tests of gravity, but predicts 0.7 $\mu$arcseconds more bending around the Sun than the Schwarzschild metric of GR. All supporting calculations are done in detail.