Some harmonic maps on pseudo-Riemannian manifolds

Rosen's bimetric theory of gravitation, when equipped with a flat background metric, is known to be realized as a harmonic mapping of Minkowski spacetime into a certain homogeneous space. This paper develops and exploits these facts to provide four classes of explicit solutions to Rosen's field equations. These four classes form the elements from which more general solutions may be formed by a type of superposition. It is also shown how spherical gravitational waves may be explicitly built into these solutions.This paper was presented at the Third Loyola Conference on Quantum Theory and Gravitation, May 29–June 1, 1985, but was received too late for inclusion in the Proceedings issue.