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. These solutions are generalisations of the spherically symmetric Majumdar-Papapetrou black hole solutions of Einstein-Maxwell gravity and are completely 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 defining the special K\"ahler manifold and the metric is expressed in terms of the symplectic invariant K\"ahler potential. The relations of the holomorphic sections to the harmonic functions constitute the generalised stabilisation equations for the moduli fields. In addition to asymptotic flatness, the harmonic functions are also constrained by the requirement that the K\"ahler connection of the underlying Hodge-K\"ahler manifold has to vanish in order to obtain static solutions. The behaviour of these solutions near the horizon is also explained.Comment: 20 pages, LaTeX, an important reference is adde

Special Geometry and Space-time Signature

We construct N=2 four and five-dimensional supergravity theories coupled to vector multiplets in various space-time signatures (t,s), where t and s refer, respectively, to the number of time and spatial dimensions. The five-dimensional supergravity theories, t+s=5, are constructed by investigating the integrability conditions arising from Killing spinor equations. The five-dimensional supergravity theories can also be obtained by reducing Hull's eleven-dimensional supergravities on a Calabi-Yau threefold. The dimensional reductions of the five-dimensional supergravities on space and time-like circles produce N=2 four-dimensional supergravity theories with signatures (t-1,s) and (t,s-1) exhibiting projective special (para)-K\"ahler geometry.Comment: 13 page

Classical Entropy of N=2 Black Holes: The minimal coupling case

We discuss the entropy and the transformation properties of classical extremal N=2 black hole solutions in supergravity theories associated with the minimal coupling models CP(n-1,1). The entropy is given by a manifestly invariant quantity under the embedding of the duality group SU(1,n) into Sp(2n+2) which is a symmetry of the classical BPS mass formula.Comment: 8 pages, Late

Phantom Metrics With Killing Spinors

We study metric solutions of Einstein-anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave equation in flat (2+1)-dimensional space-time. As examples, electric and magnetic Kasner spaces are constructed by allowing the solution to depend only on the time coordinate. Euclidean solutions are also presented.Comment: 13 page

Metrics Admitting Killing Spinors In Five Dimensions

BPS black hole configurations which break half of supersymmetry in the theory of N=2, d=5 supergravity coupled to an arbitrary number of abelian vector multiplets are discussed. A general class of solutions comprising all known BPS rotating black hole solutions is obtained.Comment: 15 pages, Late