EXACT SETS OF TEST UNCHARGED MASSIVE SPIN-3 2-FIELDS IN GENERAL-RELATIVITY/

A theorem giving the necessary and sufficient conditions for Penrose's exact sets of spinor fields in curved spacetimes is proved. An algori thm for augmenting a system of fields to an exact set and constructing covariant Taylor expansions for the fields of an exact set is propose d. The general approach is applied to test massive spin 3/2 fields. Tw o possible forms of exact sets are constructed for them on the basis o f modified Dirac-Fierz-Pauli equations. The functional arbitrariness i n the solutions of the equations for exact sets is determined. In one of the cases, the obtained exact set can be interpreted as a system of fields of spins 3/2 and 1/2 interacting through the gravitational fie ld.