New Five Dimensional Black Holes Classified by Horizon Geometry, and a Bianchi VI Braneworld

TL;DR

This paper introduces two new classes of five-dimensional static black hole solutions with horizons modeled on nilgeometry and solvegeometry, expanding the known topological types of black hole horizons and applying these solutions to Bianchi VI braneworld cosmologies.

Contribution

The paper presents novel five-dimensional vacuum Einstein solutions with non-standard horizon geometries, specifically nilgeometry and solvegeometry, not previously used in black hole models.

Findings

Horizons modeled on nilgeometry and solvegeometry.

Construction of Bianchi VI$_{-1}$ braneworld cosmologies.

Expansion of horizon topologies beyond classical types.

Abstract

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.