Instability of higher dimensional charged black holes in the de-Sitter   world
  We have shown that higher dimensional Reissner-Nordstr\"om-de Sitter black holes are gravitationally unstable for large values of the electric charge and cosmological constant in $D \geq 7$ space-time dimensions. We have found the shape of the slightly perturbed black hole at the threshold point of instability. Why only $D=4, 5$ and 6 dimensional worlds are favorable as to the black stability remains unknown. 
R. A. Konoplya, A. Zhidenko