DUALITY, CENTRAL CHARGES AND ENTROPY OF EXTREMAL BPS BLACK-HOLES

We report on some general results on the physics of extremal BPS black holes in four and five dimensions. The duality-invariant entropy-form ula for all N > 2 extended supergravities is derived. Its relation wit h the fixed-scalar condition for the black-hole ''potential energy'' w ich extremizes the BPS mass is obtained. BPS black holes preserving di fferent fractions of supersymmetry are classified in a U-duality invar iant set up. The latter deals with different orbits of the fundamental representations of the exceptional groups E-7(7) and E-6(6). We comme nt upon the interpretation of these results in a string and M-theory f ramework.