Odd-Parity Negative Modes of Einstein-Yang-Mills Black Holes and   Sphalerons
  An analytical proof of the existence of negative modes in the odd--parity perturbation sector is given for all known non-abelian Einstein--Yang--Mills black holes. The significance of the normalizability condition in the functional stability analysis is emphasized. The role of the odd--parity negative modes in the sphaleron interpretation of the Bartnik--McKinnon solutions is discussed. 
Mikhail S.Volkov and Dmitri D.Gal'tsov