EQUATIONS WITH INTRINSIC ROTATION IN GRAVITATIONAL THEORY

The generalization of the gravitational field equations is explored that give rise to the orbits of structureless (geodesic) particle motion as well as the orbits of particles with spin. In the simplest case these equations are equivalent to the Einstein equations with cosmological member of the Cartan-Killing metric of the manifold of the Anti De Sitter group, projected on the Anti De Sitter universe as base space. These equations are generally Einstein's equations with a source nonlinear in the curvature, combined with the equations suggested by C.N. Yang for a gauge theory of gravitation with third derivatives of the metric. The general case is found to be geometrically more complex, with torsion in the higher dimensional space.