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

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.

16 pages, no figures

References in corpus (5)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Plane Waves: To infinity and beyond!
• The Future of Tilted Bianchi Universes
• Automorphisms of Real 4 Dimensional Lie Algebras and the Invariant Characterization of Homogeneous 4-Spaces
• Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

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• Gravitational waves in metric-affine gravity theory
• Bianchi Class B Spacetimes with Electromagnetic Fields
• Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1
• Generalized Attractors in Five-Dimensional Gauged Supergravity
• The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)
• Homogeneous Plane-wave Spacetimes and their Stability