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

TL;DR

This paper derives new homogeneous vacuum plane-wave solutions in 4+1 dimensions and reduces them to find generalized Einstein-Maxwell and scalar field solutions in 3+1 dimensions, expanding the understanding of higher-dimensional spacetimes.

Contribution

It introduces five types of homogeneous vacuum plane-wave solutions in 4+1 dimensions and connects them to known 3+1 dimensional solutions via Kaluza-Klein reduction, including Einstein-Maxwell and scalar field cases.

Findings

Derived five types of 4+1D vacuum plane-wave solutions.

Connected higher-dimensional solutions to 3+1D Einstein-Maxwell spacetimes.

Obtained 3+1D solutions with scalar fields from higher-dimensional models.

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.