Reduction of the Poincaré gauge field equations by means of duality rotations

Abstract

A rather general procedure is developed in order to reduce the two field equations of the Poincaré gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasilinear Lagrangians of the Yang–Mills type it is shown that nontrivial torsion solutions with duality properties necessarily ‘‘live’’ on an Einstein space as metrical background.