PROLONGATION STRUCTURE AND BACKLUND-TRANSFORMATIONS OF GRAVITATIONAL DOUBLE DUALITY EQUATIONS

We derive two different Cartan differential ideals for the generalized double duality equations of gravitational gauge theories and Einstein's field equations with a cosmological constant. Using the spinor formalism for Riemann-Cartan spacetimes two different prolongations of these ideals are given. The prolongation structure will be used to construct a Backlund transformation for the coupled equations and using this general scheme the Kerr solution with dynamic torsion presented by McCrea and co-workers will be derived. Using this Kerr-de Sitter solution with dynamic torsion as a seed solution a new solution of the Poincare gauge field equations with an axial torsion part can be constructed. It turns out that this new solution leads to a vanishing Riemann-Cartan curvature and hence it is a solution of the teleparallelism theory of gravitation.