More about Vacuum Spacetimes with Toroidal Null Infinities

TL;DR

This paper classifies all solutions with toroidal null infinities within a specific class of Gowdy spacetimes, expanding understanding of vacuum solutions with such boundary conditions.

Contribution

It provides a complete construction of all solutions with toroidal null infinities in Schmidt's polarized Gowdy models, characterized by two functions of one variable.

Findings

All solutions with toroidal null infinity are explicitly constructed.

Solutions are parameterized by two smooth functions of one variable.

The analysis extends to unpolarized Gowdy models.

Abstract

Recently Bernd Schmidt has given three explicit examples of spacetimes with toroidal null infinities. In this paper all solutions with a toroidal null infinity within Schmidt's metric ansatz (polarized Gowdy models) are constructed. The members of the family are determined by two smooth functions of one variable. For the unpolarized Gowdy models the same kind of analysis carries through.