Abstract
The Newman-Penrose formalism (1962) allows a unified treatment of unquantised Weyl neutrino fields with geodesic and shear-free rays (( kappa , sigma ) fields) and of other zero rest-mass fields of type null with different spin. Taking Robinson's theorem about Maxwell null fields as a starting point, the necessary and sufficient conditions for a space-time to admit a neutrino ( kappa , sigma ) field or another null-type zero rest-mass field are given. In addition, a method of construction is developed which relates null-type fields and neutrino ( kappa , sigma ) fields with other null-type fields of different spin or, in an empty space-time, with the background conformal tensor.
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