The boundary terms in the hamiltonian, in the presence of horizons, are carefully analyzed in a simple 2D theory admitting AdS black holes. The agreement between the euclidean, Gibbons-Hawking approach and CFT through Cardy's formula is obtained modulo certain assumptions regarding the spectrum of the Virasoro's algebra. There is no discrepancy factor √ 2 once the appropriate boundary conditions are properly recognized. The results obtained here are of general validity, since they rely on general properties of black holes. In particular, the central charge can be understood as a classical result without invoking a string or any other microscopic theory. The peculiar feature of gravity, that the on-shell hamiltonian is determined by boundary terms, is the reason of the mentioned agreement.

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