  Recent numerical investigations have uncovered a surprising result:
Reissner-Nordstrom-de Sitter black holes are unstable for spacetime dimensions
larger than 6. Here we prove the existence of such instability analytically,
and we compute the timescale in the near-extremal limit. We find very good
agreement with the previous numerical results. Our results may me helpful in
shedding some light on the nature of the instability.
