Existence and uniqueness of Bowen-York Trumpets

TL;DR

This paper proves the existence of specific initial data configurations in general relativity that feature both asymptotically flat and cylindrical ends, known as trumpets, which are relevant for numerical simulations.

Contribution

It establishes the existence of trumpet geometries with combined asymptotic behaviors, advancing the mathematical understanding of initial data in numerical relativity.

Findings

Existence of initial data with trumpet geometries proven.

Construction of geometries with both flat and cylindrical ends.

Relevance for numerical relativity simulations.

Abstract

We prove the existence of initial data sets which possess an asymptotically flat and an asymptotically cylindrical end. Such geometries are known as trumpets in the community of numerical relativists.