Proof of uniqueness of the Kerr-Newman black hole solution

The electrovacuum Ernst equations are formulated as a nonlinear sigma -model on the symmetric (Kahler) space SU(1,2)/S(U(1)*U(2)). It is shown, using this formulation, that a generalised Robinson-type identity for the electrovacuum Ernst equations may be derived. A special role played in the derivation of this identity by the hidden symmetry group SU(1,2) is established. A theorem is proven that the only possible exterior solution for a (pseudo-) stationary, rotating, electrovacuum black hole with non-degenerate event horizon is the Kerr-Newman solution with m²-a²-P²-Q²>0.