Instability of Reissner-Nordstroumlm black holes in de Sitter backgrounds

Recent numerical investigations have uncovered a surprising result: Reissner-Nordstroumlm-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 time scale in the near-extremal limit. We find very good agreement with the previous numerical results. Our results may be helpful in shedding some light on the nature of the instability.