ON AXIAL-VECTOR TORSION IN VACUUM QUADRATIC POINCARE GAUGE FIELD-THEORY

The vacuum field equations of the quadratic Poincaré gauge field theory (qpgft) are solved for a purely axial vector torsion. Expressing the contortion tensor for this case as Kμνκ=ε{lunate}μνκλSλ, we prove that there are no solutions of vacuum qpgft when Sμ is non-null. However, when Sμ is null, we prove that any solution of vacuum qpgft, whose V4 part is also a solution of Einstein's vacuum field equations with a cosmological constant, is necessarily of algebraic type N. This solution has an expansion-free, shear-free and twist-free autoparallel repeated principal null congruence. © 1990.