On Global Hyperbolicity of Spacetimes: Topology Meets Functional Analysis

Abstract

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology, we continue with results of a more geometric nature, and we conclude with results that are related to current research in theoretical physics. In each case, we list a number of open questions and formulate, for a class of spacetimes, an interesting connection between global hyperbolicity of a manifold and the geodesic completeness of its corresponding space-like surfaces. This connection is substantial for the proof of essential self-adjointness of a class of pseudo differential operators, that stem from relativistic quantum field theory.

Invited contribution to the Springer Volume: Mathematical Analysis in Interdisciplinary Research

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• The causal hierarchy of spacetimes
• Some remarks on Causality Theory and Variational Methods in Lorentzian manifolds
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• Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory
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Cited by in corpus (2)

• Non-commutative coordinates from quantum gravity
• Global Hyperbolicity and Self-adjointness