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Chapter 4 - The Penrose singularity theorem

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

This chapter presents the classical Penrose singularity theorem. The main ingredients of the proof concern, on the one hand, the caussal structure of a globally hyperbolic spacetime, and on the other, differential geometry techniques involving Jacobi fields together with the Riccati and Raychaudhuri equations.

Keywords

Penrose singularity theoremRiccati equationRaychaudhuri equationfocal pointstrapped surface
Type
Chapter
Information
Lectures on Mathematical Relativity , pp. 123 - 132
Publisher: Cambridge University Press
Print publication year: 2025

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