Vacuum Plane Waves in 4+ 1 D and Exact Einstein-Maxwell solutions in 3+ 1 D

摘要: 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 which are extremely tilted.