  We find a general principle which allows one to compute the area of the
horizon of N=2 extremal black holes as an extremum of the central charge. One
considers the ADM mass equal to the central charge as a function of electric
and magnetic charges and moduli and extremizes this function in the moduli
space (a minimum corresponds to a fixed point of attraction). The extremal
value of the square of the central charge provides the area of the horizon,
which depends only on electric and magnetic charges. The doubling of unbroken
supersymmetry at the fixed point of attraction for N=2 black holes near the
horizon is derived via conformal flatness of the Bertotti-Robinson-type
geometry. These results provide an explicit model independent expression for
the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is
manifestly duality invariant. The presence of hypermultiplets in the solution
does not affect the area formula. Various examples of the general formula are
displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the
relation to the N=2 case. The entropy-area formula in five dimensions, recently
discussed in the literature, is also seen to be obtained by extremizing the 5d
central charge.

High Energy Physics - Theory