We discuss extremal under rotating black holes in N=2 supergravity coupled to vector multiplets. For the case of symmetric scalar manifolds we use group theory techniques on the coset resulting under dimensional reduction to three dimensions. We thus obtain a first order system for the scalars describing the composite non-BPS class that is characterised by a very small charge vector. Lifting back to four dimensions, we present the general solution for the single center class of black holes for arbitrary asymptotic moduli in a manifestly duality covariant way. We briefly comment on the multi center case.

Ecole Polytechnique