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

Sigbjorn Hervik
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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 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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Sigbjorn Hervik. 2003-06-02. Vacuum Plane Waves in 4+1 D and Exact solutions to Einstein's Equations in 3+1 D. https://doi.org/10.1088/0264-9381%2F20%2F19%2F312

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