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We construct perturbatively a class of charged black hole solutions in type0A string theory with higher derivative terms. They have extremal limit, wherethe solution interpolates smoothly between near horizon AdS_2 geometry and theasymptotic linear dilaton geometry. We compute the free energy and the entropyof those solution using various methods. In particular, we show that there isno correction in the leading term of the free energy in the large charge limit.This supports the duality of the type 0A strings on the extremal black hole andthe 0A matrix model in which the tree level free energy is exact without anyalpha' corrections.

Two-dimensional Black Holes in a Higher Derivative Gravity and Matrix Model