Charge orbits of symmetric special geometries and attractors

We study the critical points of the black hole scalar potential VBH in N = 2, d = 4 super-gravity coupled to n(V) vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n(V) + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kahler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n(V) + 1)-dimensional representation RV of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing quartic invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical Points Of VBH and some group theoretical considerations on homogeneous symmetric special Kahler geometry.