N=2 extremal black holes

Abstract

It is shown that extremal magnetic black hole solutions of N=2 supergravity coupled to vector multiplets ${\mathit{X}}^{\mathrm{\ensuremath{\Lambda}}}$ with a generic holomorphic prepotential F(${\mathit{X}}^{\mathrm{\ensuremath{\Lambda}}}$) can be described as supersymmetric solitons which interpolate between maximally symmetric limiting solutions at spatial infinity and the horizon. A simple exact solution is found for the special case that the ratios of the ${\mathit{X}}^{\mathrm{\ensuremath{\Lambda}}}$ are real, and it is seen that the logarithm of the conformal factor of the spatial metric equals the K\"ahler potential on the vector multiplet moduli space. Several examples are discussed in detail.