Vacuum plane waves in 4+1 D and exact solutions to Einsteins equations in 3+1 D

In this paper, we derive homogeneous vacuum plane-wave solutions to Einsteinʹs field equations in 4+1 dimensions. The solutions come in five different types of which three generalize the vacuum plane-wave solutions in 3+1 dimensions to the (4+1)dimensional case. By doing a Kaluza-Klein reduction we obtain solutions to the Einstein-Maxwell equations in 3+1 dimensions. The solutions generalize the vacuum plane-wave spacetimes of Bianchi class B to the non-vacuum case and describe spatially homogeneous spacetimes containing an extremely tilted fluid. Also, using a similar reduction we obtain (3+1)-dimensional solutions to the Einstein equations with a scalar field.