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 $D\ge 7$ 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.