The Hesse potential, the c-map and black hole solutions

We present a new formulation of the local c-map, which makes use of the real formulation of special Kahler geometry and the associated Hesse potential. As an application we use the temporal version of the c-map to derive the black hole attractor equations from geometric properties of the scalar manifold, and we construct various stationary solutions for four-dimensional vector multiplets by lifting instanton solutions of the time-reduced theory.Comment: 76 pages. Second revised version: substantial extension. Further references added and discussion extended. Construction of axion-free non-BPS extremal solutions for a class of non-homogeneous target spaces added. Accepted for publication in JHE