EXTREMAL BLACK HOLES AND NILPOTENT ORBITS

The stationary solutions of a large variety of (super)gravity theories can be described within a non-linear sigma model R/h* coupled to Euclidean gravity in three-dimensions, for which R 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 R 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 extrernal black holes must lie in a certain Lagrangian submanifold of a nilpotent orbit of R. 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.