Special Vinberg cones and the entropy of BPS extremal black holes

A bstract We consider the static, spherically symmetric and asymptotically flat BPS extremal black holes in ungauged N = 2 D 4 supergravity theories, which scalar manifold of vector multiplets is homogeneous. By a result Shmakova on attractor equations, entropy this kind can be expressed only terms their electric magnetic charges, provided that inverse certain quadratic map (uniquely determined by prepotential theory) given. This was previously known just for cases theory homogeneous space. In paper we use Vinberg’s cones to determine an explicit expression such inverse, under assumption homogeneous, but not necessarily symmetric. As immediate consequence, get formula holds any model with manifold.