  A new proof of the uniqueness of the Kerr-Newman black hole solutions amongst
asymptotically flat, stationary and axisymmetric electro-vacuum spacetimes
surrounding a connected Killing horizon is given by means of an explicit
construction of the corresponding complex Ernst potentials on the axis of
symmetry. This construction, which makes use of the inverse scattering method,
also works in the case of a degenerate horizon.
