On the linear stability of the extreme Kerr black hole under axially   symmetric perturbations
  We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the particular case of Minkowski, using this energy we also prove pointwise boundedness of the perturbation in a remarkable simple way. 
Sergio Dain and Ivan Gentile de Austria
gr-qc