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 is proved for spinorial fields in curved spacetimes. The algorithm is proposed for supplementation for fields set up to exact set and for calculation of Taylor expansions for fields from such exact set. The general approach is applied to study test massive spin 3/2 fields. Two different exact sets are possible for such fields satisfying the modified Dirac–Fierz–Pauli equations. They are constructed and their functional freedom is calculated. One of the found sets may be interpreted as the set for interacting spin 3/2 and spin 1/2 fields in curved spacetime.