Solvegeometry gravitational waves

In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein solvmanifolds (i.e., solvable Lie groups considered as manifolds) constructed in a previous paper as a starting point, we show that there also exist solvegeometry gravitational waves. Some geometric aspects are discussed and examples of spacetimes having additional symmetries are given, for example, spacetimes generalising the Kaigorodov solution. The solvegeometry gravitational waves are also examples of spacetimes which are indistinguishable by considering the scalar curvature invariants alone.