Some properties of higher spin rest-mass zero fields in general relativity

Abstract

The propagation of a zero rest-mass test field of arbitrary spins>1 through curved space-time is found to be subject to strong constraints. A null test field is shown to be possible only in a restricted class of spaces previously introduced by Kundt and Thompson. This result is in fact a simultaneous generalization of the theorems of Robinson and of Goldberg and Sachs. For test fields of spin-2 in vacuum spaces, solutions of the propagation equation are restricted, save in a few exceptional cases, to constant multiples of the Weyl spinor. The exceptional cases are discussed, and appear to be physically uninteresting.