The general relativistic infinite plane

TL;DR

This paper compares two general relativistic models of an infinite plane with finite mass, analyzing their properties and deviations from Newtonian gravity to enhance understanding of Einstein's equations.

Contribution

It introduces and analyzes two relativistic metrics for the infinite plane, connecting classical intuition with modern research models.

Findings

The brane world metric and domain wall metric differ in their gravitational field representations.

Both models provide educational insights into Einstein's field equations.

The study highlights deviations from Newtonian predictions in relativistic contexts.

Abstract

Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics or Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. In this article we examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. The first metric is the 4D version of the 5D "brane" world models which are the starting point for many current research papers. The second case is the cosmological domain wall metric. We examine to what extent these different metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide the beginning student in general relativity both computational practice and conceptual insight into Einstein's field equations. In addition they do this by introducing the student to material that is at the forefront of current research.