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General Relativity and the Einstein Equations$
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Yvonne Choquet-Bruhat

Print publication date: 2008

Print ISBN-13: 9780199230723

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230723.001.0001

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Singularities

Singularities

Chapter:
(p.402) XIII Singularities
Source:
General Relativity and the Einstein Equations
Author(s):

Yvonne Choquet-Bruhat

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230723.003.0013

This chapter presents a computable sufficient condition for the future causal completeness of a spacetime, and then a sufficient condition for its future or null incompleteness. It gives the fundamentals of the definitions pertinent to the study of incompleteness of spacetimes by the geometric methods introduced and developed by Penrose, Hawking, and their followers. It provides some elements of black hole theory and comments on Penrose's weak cosmic censorship conjecture, which says essentially that singularities developing from smooth initial data are hidden inside black holes. The conjecture is not easy to make mathematically precise without impoverishing its possible physical content. The chapter analyzes the study by Christodoulou of the singularities in spherically symmetric solutions of the Einstein-scalar equations. An up-to-date survey of results on the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture is presented. Finally, how the Fuchs theorem permits the analysis of some types of initial (Big Bang) singularities occurring in solutions of the Einstein equations, called asymptotically velocity term dominated (AVTD) behavior, is discussed.

Keywords:   spacetime, incompleteness, BKL conjectuve, AVTD, black hole

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