Some zero rest mass test fields in general relativity

Abstract

Zero rest mass test fields of pure algebraic type are defined and studied via the newly developed GHP formalism. The field equations are written explicitly and an immediate generalisation of Robinson's theorem is obtained. The form for the general zero rest mass test field of pure type is determined in terms of the tetrad components of the background Weyl spinor and an additional gauge dependent function which can be thought of as representing a test neutrino field.