I know that the Israel theorem accounts for only non-rotating, non-electrically charged black holes, but as I understand the theorem was then generalized for rotating and charged black holes. And, as I understand the no-hair theorem would basically implies that every static black hole solution to Einstein Equations cam be completely caracterized by the mass, charge and the absolute value of its intrinsic angular momentum. But the no-hair theorem is usually called a conjecture, so what assumptions are necessary in the generalized Israel theorems that must be overcome so that they can become the full no-hair theorem? (Spherical symmetry? Perturbed spherical symmetry? full analiticity of the space time?)