Principal null directions of the neutrino and derived Maxwell fields

Abstract

Bineutrino fields are constructed from neutrinos described by the two-component Weyl equation. If we demand that the bineutrino fields fulfil the set of Maxwell equations, we have a classical version of the “neutrino theory of light”. With the help of the spin coefficient formalism, it is established that the energy tensor of the neutrino fields cannot be positively definite, and that the principal null direction of the bineutrino Maxwell fields does not coincide with the principal null direction of the underlying neutrino fields.