Static plane symmetric relativistic fluids and empty repelling singular boundaries

TL;DR

This paper analyzes a static, plane symmetric relativistic fluid solution in Einstein's equations, revealing a unique matter-free repelling boundary where all geodesics bounce, highlighting unusual spacetime properties.

Contribution

It provides a detailed exact solution with a novel matter-free boundary that repels matter, and explores its geodesic behavior.

Findings

Presence of a matter-free repelling singular boundary

All geodesics bounce off this boundary

Unique properties of the spacetime geometry

Abstract

We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that this simple spacetime exhibits very curious properties. In particular, it has a free of matter repelling singular boundary and all geodesics bounce off it.