Gluing variations

TL;DR

This paper investigates methods for extending and embedding geometric structures in vacuum spacetimes with a cosmological constant across various dimensions, focusing on characteristic data and introducing submanifold-data of order k.

Contribution

It introduces the concept of submanifold-data of order k and proves that vacuum Cauchy data on a boundary can always be extended beyond it in vacuum spacetimes.

Findings

Extension of vacuum Cauchy data beyond boundaries.

Introduction of submanifold-data of order k.

Results applicable in any spacetime dimension d ≥ 4.

Abstract

We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions $d\ge 4$, with emphasis on characteristic data. A useful tool is provided by the notion of submanifold-data of order $k$. As an application of our methods we prove that vacuum Cauchy data on a spacelike Cauchy surface with boundary can always be extended to vacuum data defined beyond the boundary.