HKT Geometry and de Sitter Supergravity

TL;DR

This paper classifies solutions in five-dimensional de Sitter supergravity with Killing spinors, linking them to hyper-Kahler torsion manifolds and providing explicit examples like multi-BMPV black holes in an expanding universe.

Contribution

It demonstrates how timelike solutions relate to HKT manifolds and constructs new solutions using Einstein-Weyl geometry, extending the understanding of de Sitter supergravity configurations.

Findings

Timelike solutions are determined by 4D HKT manifolds.

Conformally hyper-Kahler HKT manifolds yield solutions from ungauged supergravity.

Explicit multi-BMPV de Sitter black hole solutions are constructed.

Abstract

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-Kahler torsion (HKT) manifold. If the HKT manifold is conformally hyper-Kahler 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-Kahler, examples admitting a tri-holomorphic Killing vector field are constructed in terms of certain solutions of three dimensional Einstein-Weyl geometry.