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 5 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. e-mail: [email protected]. Address after 1 Sept., 2000: Dept. of Physics, University of Alberta, Edmonton, AB, Canada T6G 2J1. e-mail: [email protected]