The general relativistic infinite plane

Uniform fields are one of the simplest and most pedagogically useful examples in introductory courses on electrostatics and Newtonian gravity. In general relativity there have been several proposals as to what constitutes a uniform field. We examine two metrics that can be considered the general relativistic version of the infinite plane with finite mass per unit area. One metric is the four-dimensional version of the five-dimensional “brane” world models of current interest. Another metric is the cosmological domain wall metric. We examine to what extent these metrics match or deviate from our Newtonian intuition about the gravitational field of an infinite plane. These solutions provide beginning students in general relativity both computational experience and conceptual insight into Einstein’s field equations and introduce them to material that is at the forefront of current research.