Behavior of Einstein-Rosen Waves at Null Infinity

TL;DR

This paper investigates the asymptotic behavior of Einstein-Rosen waves at null infinity, revealing directional differences in decay rates and providing a geometric explanation through symmetry reduction.

Contribution

It offers a comprehensive analysis of Einstein-Rosen waves at null infinity in all directions, highlighting unexpected directional behavior and its geometric origin.

Findings

Behavior in generic directions is better than orthogonal directions.

The geometric origin of directional differences is clarified via 3D symmetry reduction.

Provides insights into wave decay properties at null infinity.

Abstract

The asymptotic behavior of Einstein-Rosen waves at null infinity in 4 dimensions is investigated in {\it all} directions by exploiting the relation between the 4-dimensional space-time and the 3-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is {\it better} than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be understood most clearly from the 3-dimensional perspective.