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Chapter 3 - Basics of Lorentzian causality

Published online by Cambridge University Press:  03 April 2025

Justin Corvino  and
Pengzi Miao
Justin Corvino
Affiliation:
Lafayette College, Pennsylvania
Pengzi Miao
Affiliation:
University of Miami
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Summary

The tangent space at any point on a Lorentzian manifold can be partitioned into three classes, timelike, null and spacelike vectors, from which the causal structure derives. In this chapter we introduce some basic concepts of Lorentzian causality needed in the discussion of the Penrose singularity theorem in the next chapter.

Keywords

causal structureglobally hyperbolic spacetimeachronal setCauchy hypersurfaceCauchy development
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Chapter
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Lectures on Mathematical Relativity , pp. 107 - 122
Publisher: Cambridge University Press
Print publication year: 2025

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