Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes

TL;DR

This paper proves the existence of a second Cauchy horizon in S2xS1 Gowdy spacetimes with a regular past horizon, establishing a universal relation between horizon areas and a conserved quantity.

Contribution

It provides an explicit metric expression for the future horizon and demonstrates a universal area relation linked to a conserved quantity J.

Findings

Existence of a second Cauchy horizon when J ≠ 0

Explicit metric form on the future horizon derived

Universal relation A_p A_f = (8π J)^2 established

Abstract

We study general S2xS1 Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity $J$ is not zero. We derive an explicit expression for the metric form on the future Cauchy horizon in terms of the initial data on the past horizon and conclude the universal relation $A\p A\f=(8\pi J)^2$ where $A\p$ and $A\f$ are the areas of past and future Cauchy horizon respectively.