  The stationary solutions of a large variety of (super)gravity theories can be
described within a non-linear sigma model G / H* coupled to Euclidean gravity
in three-dimensions, for which G is a simple group and H* a non-compact real
form of its maximal compact subgroup. The absence of naked singularities in
four dimensions requires the G Noether charge in 3D to satisfy a characteristic
equation that determines it in function of the mass, the NUT charge and the
electro-magnetic charges of the solution. It follows that the Noether charge
associated to extremal black holes must lie in a certain Lagrangian submanifold
of a nilpotent orbit of G. Constructing a suitable parameterisation of this
Lagrangian, we are able to determine the so-called `fake superpotential' that
governs the radial dependency of the scalar fields.
