On some properties of the Attractor Equations
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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 Kähler 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 Kähler gauge and its relevance for the recently discussed entropic functional.
14 pages, to be published in Phys. Lett. B; a misprint in Ref. [13] has been corrected
14 pages, to be published in Phys. Lett. B; a misprint in Ref. [13] has been corrected