100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

CHAPTER 3THE NATURE OF SPACETIME SINGULARITIESALAN D. RENDALLMax-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutAm Mühlenberg 1, D14476 Golm, GermanyPresent knowledge about the nature of spacetime singularities in thecontext of classical general relativity is surveyed. The status of the BKLpicture of cosmological singularities and its relevance to the cosmic censorshiphypothesis are discussed. It is shown how insights on cosmiccensorship also arise in connection with the idea of weak null singularitiesinside black holes. Other topics covered include matter singularitiesand critical collapse. Remarks are made on possible future directions inresearch on spacetime singularities.1. IntroductionThe issue of spacetime singularities arose very early in the history of generalrelativity and it seems that Einstein himself had an ambiguous relationshipto singularities. A useful source of information on the confusion surroundingthe subject in the first half century of general relativity is Ref. 1. The presentarticle is a survey of the understanding we have of spacetime singularitiestoday.Before concentrating on general relativity, it is useful to think moregenerally about the concept of a singularity in a physical theory. In thefollowing the emphasis is on classical field theories although some of thediscussion may be of relevance to quantum theory as well. When a physicalsystem is modelled within a classical field theory, solutions of the fieldequations are considered. If it happens that at some time physically relevantquantities become infinite at some point of space then we say that thereis a singularity. Since the physical theory ceases to make sense when basicquantities become infinite a singularity is a sign that the theory has been76