Taub's plane-symmetric vacuum spacetime revisited

TL;DR

This paper revisits Taub's plane-symmetric vacuum solution, clarifying its properties, asymptotic structure, and interpretation as a negative mass exterior gravitational field, with connections to cosmological models.

Contribution

It provides a clearer physical interpretation of Taub's solution, including new insights into its asymptotic behavior, matching conditions, and source nature.

Findings

Taub's solution represents a negative mass exterior field.

The solution's asymptotic structure is characterized.

Connections to Kasner's cosmological model are discussed.

Abstract

The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without 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 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 {\em negative} mass distribution, confirming previous statements to that effect in the literature. Some analogies to Kasner's spatially homogeneous cosmological model are also referred to.