BLACK-HOLES IN N=2 SUPERGRAVITY THEORIES AND HARMONIC-FUNCTIONS

We present dyonic BPS static black hole solutions for general d = 4, N = 2 supergravity theories coupled to vector and hypermultiplets. Thes e solutions are generalisations of the spherically symmetric Majumdar- Papapetrou black hole solutions of Einstein-Maxwell gravity and are co mpletely characterised by a set of constrained harmonic functions. In terms of the underlying special geometry, these harmonic functions are identified with the imaginary part of the holomorphic sections defini ng the special Kahler manifold and the metric is expressed in terms of the symplectic invariant Kahler potential. The relations of the holom orphic sections to the harmonic functions constitute the ''generalised stabilisation equations'' for the moduli fields, In addition to asymp totic flatness, the harmonic functions are also constrained by the req uirement that the Kahler connection of the underlying Hodge-Kahler man ifold has to vanish in order to obtain static solutions. The behaviour of these solutions near the horizon is also explained. (C) 1998 Elsev ier Science B.V.