7 research outputs found
Special geometry of Euclidean supersymmetry IV:the local c-map
We consider timelike and spacelike reductions of 4D, N = 2 Minkowskian and Euclidean vector multiplets coupled to supergravity and the maps induced on the scalar geometry. In particular, we investigate (i) the (standard) spatial c-map, (ii) the temporal c-map, which corresponds to the reduction of the Minkowskian theory over time, and (iii) the Euclidean c-map, which corresponds to the reduction of the Euclidean theory over space. In the last two cases we prove that the target manifold is para-quaternionic Kahler. In cases (i) and (ii) we construct two integrable complex structures on the target manifold, one of which belongs to the quaternionic and para-quaternionic structure, respectively. In case (iii) we construct two integrable para-complex structures, one of which belongs to the para-quaternionic structure. In addition we provide a new global construction of the spatial, temporal and Euclidean c-maps, and separately consider a description of the target manifold as a fibre bundle over a projective special Kahler or para-Kahler base
Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
We present a method which allows to deform extremal black hole solutions into
non-extremal solutions, for a large class of supersymmetric and
non-supersymmetric Einstein-Vector-Scalar type theories. The deformation is
shown to be largely independent of the details of the matter sector. While the
line element is dressed with an additional harmonic function, the attractor
equations for the scalars remain unmodified in suitable coordinates, and the
values of the scalar fields on the outer and inner horizon are obtained from
their fixed point values by making specific substitutions for the charges. For
a subclass of models, which includes the five-dimensional STU-model, we find
explicit solutions.Comment: 33 page
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