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In the weak field approximation, the nonsymmetric gravitational theory has, in addition to the Newtonian gravitational potential, a Yukawa potential produced by the exchange of a spin boson between fermions. If the range is of order kpc, then the potential due to the interaction of known neutrinos in the halos of galaxies can explain the flat rotation curves of galaxies. The results are based on a physical linear approximation to the NGT field equations and they are consistent with equivalence principle observations, other solar system gravitational experiments and the binary pulsar data.

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