Spin Flavor Oscillation of Neutrinos in Rotating Gravitational Fields and Their Effects on Pulsar Kicks

The origin of high velocities of pulsars is studied by considering the spin-flip conversion of neutrinos propagating in a gravitational field of a protoneutron star. For a rotating gravitational source (such as pulsars) with angular velocity ${\bm \omega}$, one finds that the spin connections (entering in the Dirac equation written in curved space time) induce an additional contribution to neutrino energy which is proportional to ${\bm \omega}\cdot {\bf p}$, with ${\bf p}$ the neutrino momentum. Such a coupling (spin-gravity coupling) can be responsible of pulsar kicks being the asymmetry of the neutrino emission generated by the relative orientation of the neutrino momentum ${\bf p}$ with respect to the angular velocity ${\bm \omega}$. As a consequence, the mechanism suggests that the motion of pulsars is correlated to their angular velocity ${\bm \omega}$. In this work we consider neutrinos propagating orthogonally to the magnetic field. As in the usual approaches,spin flip conversion is generated via the coupling of the neutrino magnetic momentum with the magnetic field. For our estimations, we use the large non-standard neutrino magnetic momentum provided by astrophysical and cosmological constraints, $\mu_\nu\sim 10^{-11}\mu_B$. The connection with recent observations and statistical analysis is also discussed.