Extremal black holes, nilpotent orbits and the true fake superpotential

Understand

Dimensional reduction along time offers a powerful way to study stationary solutions of 4D symmetric supergravity models via group-theoretical methods.

• We apply this approach systematically to extremal, BPS and non-BPS, spherically symmetric black holes, and obtain their "fake superpotential" W.
• The latter provides first order equations for the radial problem, governs the mass and entropy formula and gives the semi-classical approximation to the radial wave function.
• To achieve this goal, we note that the Noether charge for the radial evolution must lie in a certain Lagrangian submanifold of a nilpotent orbit of the 3D continuous duality group, and construct a suitable parametrization of this Lagrangian.