Taub’s plane-symmetric vacuum spacetime reexamined

Abstract

The gravitational properties of the only static plane-symmetric vacuum solution of Einstein's field equations without a cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field limit, and pertainment to the Schwarzschild family of spacetimes) are reviewed in a physically much more transparent way, as well as new results about its asymptotic structure, possible matchings, and the nature of the source are furnished. The main results point to the fact that the solution must be interpreted as representing the exterior gravitational field due to a negative mass distribution, confirming previous statements to that effect in the literature. Some analogies to Kasner's spatially homogeneous cosmological model are also mentioned.