  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 generalise 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 generalise
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.
