On the sources of static plane symmetric vacuum space-times

TL;DR

This paper examines the sources of static plane symmetric vacuum space-times, identifying the energy condition properties of the Taub and Rindler solutions and discussing their physical interpretations.

Contribution

It provides a detailed analysis of the sources for the Taub and Rindler solutions under reflection symmetry, highlighting their energy condition compliance and physical significance.

Findings

Taub solution source does not satisfy energy conditions.

Rindler solution source satisfies weak and strong energy conditions.

Rindler solution models a uniform gravitational field.

Abstract

The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy conditions, which is consistent with previous studies, while the source for the Rindler solution satisfies the weak and strong energy conditions (but not the dominant one). It is argued that the counterpart of the Einstein theory to the gravitational field of a massive Newtonian plane should be described by the Rindler solution, which represents also a uniform gravitational field.