NEW MASSLESS FREE FIELDS IN OLD SPACETIMES

A kind of massless free field, a 'symmetric recurrent' spinor field is defined. The principal spinors of such a field define shear-free ray congruences. A vacuum solution of Einstein's equations is of type {2, 2}, {4} or conformally flat iff its Weyl spinor is symmetric recurrent . The massless free fields of the Robinson-Sommers theorem are symmetr ic recurrent. A spacetime with a certain kind of symmetric recurrent s pinor admits a Killing spinor. A massless free field associated with a Killing spinor is symmetric recurrent. Symmetric recurrent fields are constructed for spacetimes with certain types of Killing spinor, esse ntially one per Killing spinor.