The structure of the space solutions of Einstein's equations: II Several Killing fields and the Einstein-Yang-Mills equations

Arms, J. M., J. E. Marsden and V. Moncrief

Ann. Physics, 144, (1982), 81-106

Abstract:

The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members.