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

On the instability of Reissner-Nordstrom black holes in de Sitter backgrounds