On the existence of neutrino ’’zero-modes’’ in vacuum spacetimes

Abstract

Neutrino ’’zero modes’’ in curved spacetime, the analog of static solutions of the neutrino equation in flat space, are defined as the kernel of an elliptic operator obtained from a ’’3+1’’ decomposition of the neutrino equation relative to a spacelike hypersurface. In this paper, vacuum, globally hyperbolic spacetimes that admit ’’zero modes’’ are characterized.