Neutrino Fields in a Sandwich Gravitational Wave Background

Sandwich gravitational waves are given globally in terms of step functions at the boundaries. Linearized Einstein-Weyl equations are solved exactly in this background in Rosen coordinates. Depending on the geometry and composition of the sandwich wave, the neutrino's energy-momentum redistributes itself. At the test field level, since the background will not change, the neutrino's energy density in particular will show variations between positive and negative extrema when crossing the sandwich wave. This may reveal facts about the weakly interacting neutrinos in cosmology.