N-dimensional plane symmetric solution with perfect fluid source

TL;DR

This paper presents a new n-dimensional plane symmetric solution to Einstein's equations with a perfect fluid source, generalizing previous 4D solutions and analyzing its symmetry, energy conditions, and boundary matching.

Contribution

It introduces a novel n-dimensional solution with specific symmetries and energy condition analysis, extending prior 4D models to higher dimensions.

Findings

Solution exists for n ≥ 4 with specified symmetries.

Energy conditions constrain parameter regions.

Boundary matching to known metrics is feasible.

Abstract

A new class of plane symmetric solution sourced by a perfect fluid is found in our recent work. An n-dimensional ($n\geq 4$) global plane symmetric solution of Einstein field equation generated by a perfect fluid source is investigated, which is the direct generalization of our previous 4-dimensional solution. One time-like Killing vector and $(n-2)(n-1)/2$ space-like Killing vectors, which span a Euclidean group $G_{(n-2)(n-1)/2}$, are permitted in this solution. The regions of the parameters constrained by weak, strong and dominant energy conditions for the source are studied. The boundary condition to match to n-dimensional Taub metric and Minkowski metric are analyzed respectively.