Anisotropic neutrino emission during the neutron star formation can be the origin of the observed proper motions of pulsars. We derive a general expression for the momentum asymmetry in terms of the neutrino energy flux gradient, and show that a nonvanishing effect is induced at the lowest order by a deformed neutrinosphere. In particular, this result is valid for a neutrino flux transported through a spherical atmosphere with constant luminosity.Comment: 11 pages, added appendix, references, and minor changes in section 1, 2, and

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In this work we propose an extended formulation for the interaction between neutrinos and gravitational fields. It is based on the parametrized post-Newtonian approach, and includes a violation of the universality of the gravitational interaction which is nondiagonal in weak flavor space. We find new effects that are not considered in the standard scenario for violation of the equivalence principle. They are of the same order as the effects produced by the Newtonian potential, but they are highly directional dependent and could provide a very clean test of that violation. Phenomenological consequences are briefly discussed.

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