Abstract
We examine the conjecture that black holes violating the reverse isoperimetric inequality have negative specific heat at constant volume CV [1]. We test this conjecture on the family of generalized exotic Bañados, Teitelboim and Zanelli (BTZ) black holes and find that CV can be positive even when the reverse isoperimetric inequality is violated, providing a counter example to the conjecture. However in all cases where CV is positive, the specific heat at constant pressure CP is negative, indicating that generalized exotic black holes are thermodynamically unstable, suggesting that a broader version of the conjecture might hold.
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