Gravitational coupling of neutrinos to matter vorticity II: microscopic asymmetries in angular-momentum modes

The gravitational coupling of neutrinos to matter vorticity is examined; in the context of the Einstein's theory of gravitation and for technical simplicity considered the Goedel model as the gravitational background, whose matter content has a non-null vorticity has been considered. Dirac's equation is solved by separation of the neutrino amplitudes into invariant angular-momentum and energy modes. These modes provide two distinct representation bases for the algebra of the total angular momentum of the system (one finite-dimensional and the other infinite-dimensional). The presence of a vorticity field of matter generates, via gravitation, microscopic asymmetries in neutrino physics. The angular momentum space appears to be polarized along the direction determined by the local vorticity field Ω sup(→). At the microscopic level, currents are asymmetric along the direction determined by the vorticity field: Neutrino (anti neutrino) currents are larger along the direction antiparallel (parallel) to the vorticity field. In the case of production of pairs under CP violation a net number asymmetry may be generated between neutrinos and antineutrinos. (Author)