Duality symmetry and the Cardy limit

We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 x T-2, with duality group O(6,22, Z) x SL(2, Z). In the Cardy limit an internal circle combines with the AdS(2) component in the near horizon geometry to give a BTZ black hole whose entropy is given by the Cardy formula. We study black holes carrying D0 - D4 and D0 - D6 brane charges. We find, both in the supersymmetric and non-supersymmetric cases, that a generic set of charges cannot be brought to the Cardy limit using the duality symmetries. In the non-supersymmetric case, unlike the supersymmetric one, we find that when the charges are large, a small fractional change in them always allows the charges to be taken to the Cardy limit. These results could lead to a microscopic determination of the entropy for extremal non-supersymmetric black holes, including rotating cases like the extreme Kerr black hole in four dimensions.