Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D

Details Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D

2002-10-23

arxiv.org/abs/gr-qc/0210080v2

Class.Quant.Grav.20:4315-4327,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figures

Scientific paper

10.1088/0264-9381/20/19/312

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.

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