
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 , with emphasis on characteristic data. A useful tool is provided by the notion of submanifold-data of order . 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.
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Taxonomy
TopicsCosmology and Gravitation Theories · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research
