Existence and construction of neutrino fields with geodesic and shear-free rays and of other zero rest-mass fields in curved space-time

The Newman-Penrose formalism allows a unified treatment of unquantized Weyl neutrino fields with geodesic and shear-free rays ((kappa, sigma) fields) and other zero rest-mass fields of type null with different spin. Taking Robinson's theorem (J. Math. Phys.; 2: 290 (1961)) 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 related 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. (author)