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We study the propagation of Dirac neutrinos in gravitational backgrounds and show that the gravitational interaction can lead to neutrino asymmetry due to modifications in dispersion relation. We give some examples of spacetime geometries where such asymmetry can arise. This asymmetry would have contributed to the relic neutrino asymmetry through the interaction of neutrinos with primordial black holes before neutrinos decoupled. In the present epoch it may be generated in accretion around high temperature rotating black holes.doi:10.1142/s0217732303009691 fatcat:6xa7jjxum5dxzjm36xc54inoji