On some properties of the attractor equations

We discuss the attractor equations of N = 2, d = 4 supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS attractor solutions correspond to the vanishing determinant of a (fermionic) gaugino mass matrix. The stability of these solutions is controlled by the data of the underlying special Kahler geometry of the vector multiplets' moduli space. Finally, after analyzing the 1-modulus case more in detail, we briefly comment on the choice of the Kahler gauge and its relevance for the recently discussed entropic functional. (c) 2006 Published by Elsevier B.V.