Initial data engineering

TL;DR

This paper introduces a new local gluing method for general relativistic initial data sets that relaxes previous constraints, enabling the construction of diverse space-times without global conditions.

Contribution

It develops a novel gluing construction applicable to generic initial data, removing assumptions like constant mean curvature near gluing points and global restrictions.

Findings

Constructs initial data sets without global conditions.

Proves existence of certain vacuum space-times.

Extends previous gluing techniques to more general settings.

Abstract

We present a local gluing construction for general relativistic initial data sets. The method applies to generic initial data, in a sense which is made precise. In particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points, which was the case for previous such constructions. No global conditions on the initial data sets such as compactness, completeness, or asymptotic conditions are imposed. As an application, we prove existence of spatially compact, maximal globally hyperbolic, vacuum space-times without any closed constant mean curvature spacelike hypersurface.