THE UNIQUENESS THEOREM FOR ROTATING BLACK-HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC-MAPPINGS

We consider rotating black hole configurations of self-gravitating map s from spacetime into arbitrary Riemannian manifolds. We first establi sh the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restri cting ourselves to mappings with harmonic action, we subsequently prov e that the only stationary and axisymmetric, asymptotically flat black hole solution with a regular event horizon is the Kerr metric. Togeth er with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr f amily amongst all stationary black hole solutions of self-gravitating harmonic mappings.