On the Moduli Space of non-BPS Attractors for N = 2 Symmetric Manifolds

We study the “flat” directions of non-BPS extremal black hole attractors for N = 2, d = 4 supergravities whose vector multiplets’ scalar manifold is endowed with homogeneous symmetric special Kähler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d = 5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kähler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N = 2, d = 5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.