New five-dimensional black holes classified by horizon geometry, and a Bianchi VI braneworld

We introduce two new families of solutions to the vacuum Einstein equations with negative cosmological constant in five dimensions. These solutions are static black holes whose horizons are modelled on the 3-geometries nilgeometry and solvegeometry. Thus the horizons (and the exterior spacetimes) can be foliated by compact 3-manifolds that are neither spherical, toroidal, hyperbolic, nor product manifolds, and therefore are of a topological type not previously encountered in black hole solutions. As an application, we use the solvegeometry solutions to construct Bianchi VI-1 braneworld cosmologies.