The application of spin coefficient techniques in the vacuum quadratic Poincaré gauge field theory

The vacuum field equations of the quadratic Poincaré gauge field theory are expressed in the spin coefficient formalism of Newman and Penrose. These are differential identities involving curvature and torsion and, for an NP-type approach, must be combined with the NP-identities in aU ₄ given by Jogia and Griffiths (1980). The use of the formalism is demonstrated in the derivation of some new exact solutions.