MACROSCOPIC ENTROPY OF N=2 EXTREMAL BLACK-HOLES

Extremal BPS-saturated black holes in N = 2, d = 4 supergravity can ca rry electric and magnetic charges (q((m))(boolean AND),q(boolean AND)( (e)). It is shown that in smooth cases the moduli fields at the horizo n take a fixed ''rational'' value X(boolean AND)(q((m)), q((e))) which is determined by the charges and is independent of the asymptotic val ues of the moduli fields. A universal formula for the Bekenstein-Hawki ng entropy is derived in terms of the charges and the moduli space geo metry al X(boolean AND)(q((m)), q((e))). This work extends previous re sults of Ferrara, Kallosh and the author for the pure magnetic case.