Half polarized U(1) symmetric vacuum spacetimes with AVTD behavior

TL;DR

This paper introduces the half polarization condition for U(1) symmetric vacuum spacetimes, establishing when they exhibit AVTD behavior near singularities, extending previous polarization results.

Contribution

It identifies a necessary and sufficient half polarization condition for AVTD behavior in U(1) symmetric vacuum spacetimes, broadening understanding of singularity behavior.

Findings

Half polarization condition characterizes AVTD behavior.

Extension from polarized to half polarized U(1) solutions.

Provides criteria for singularity analysis in vacuum spacetimes.

Abstract

In a previous work, we used a polarization condition to show that there is a family of U(1) symmetric solutions of the vacuum Einstein equations such that each exhibits AVTD (Asymptotic Velocity Term Dominated) behavior in the neighborhood of its singularity. Here we consider the general case of U(1) bundles and determine a condition, called the half polarization condition, necessary and sufficient in our context, for AVTD behavior near the singularity.