Smooth Gowdy symmetric generalized Taub-NUT solutions

TL;DR

This paper proves the existence of smooth Gowdy symmetric generalized Taub-NUT solutions with a regular past horizon, showing that a future horizon typically exists and providing explicit metric expressions based on initial data.

Contribution

It introduces a new class of solutions with a regular past horizon and derives explicit formulas for the future horizon metric, extending previous Gowdy model results.

Findings

Existence of solutions with regular past Cauchy horizon

Future Cauchy horizon exists for generic data

Explicit metric expression for the future horizon

Abstract

We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In particular, we prove existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. The result of our investigations is that a future Cauchy horizon exists for generic asymptotic data. Moreover, we derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S2xS1 Gowdy models.