Brill Waves with Slow Fall-Off Towards Spatial Infinity

TL;DR

This paper investigates Brill wave solutions to Einstein's vacuum equations with slow fall-off at spatial infinity, proving their existence and uniqueness, and providing numerical examples including non-symmetric cases.

Contribution

It introduces a new class of Brill wave solutions with slow fall-off, establishing their mathematical properties and providing explicit numerical examples.

Findings

Existence and uniqueness of solutions with slow fall-off

Numerical construction of representative solutions

Example of a non-symmetric solution at infinity

Abstract

We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some representative solutions. We numerically construct an explicit example with slow-off which does not exhibit antipodal symmetry at spatial infinity.