HKT geometry and de Sitter supergravity

Solutions of five-dimensional minimal de Sitter supergravity admitting Killing spinors are considered. It is shown that the “timelike” solutions are determined in terms of a four-dimensional hyper-Kähler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kähler the most general solution can be obtained from a sub-class of supersymmetric solutions of minimal N=2 ungauged supergravity, by means of a simple transformation. Examples include a multi-BMPV de Sitter solution, describing multiple rotating black holes co-moving with the expansion of the universe. If the HKT manifold is not conformally hyper-Kähler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three-dimensional Einstein-Weyl geometry.