Abstract. In this paper, we derive homogeneous vacuum plane-wave solutions to Einstein's 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.

PACS numbers: 04.50.+h, 04.20.Jb, 98.80.Jk

Print publication: Issue 19 (7 October 2003)
Received 2 June 2003
Published 2 September 2003