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

The Nature of Spacetime Singularities 89been exerted by the picture of Belinskii, Khalatnikov and Lifshitz (BKL). Inthe case of black hole singularities the old idea that they should be similarto cosmological singularities has been replaced by the new paradigm ofweak null singularities due to Poisson and Israel. A new kind of singularityhas emerged in the work of Choptuik on critical collapse. It remains to beseen whether the Einstein equations have further types of singularities instore for us.New things can happen if we go beyond the usual framework of thesingularity theorems. The cosmological acceleration which is now wellestablishedby astronomical observations corresponds on the theoreticallevel to a violation of the strong energy condition and suggests that a reworkingof the singularity theorems in a more general context is necessary.Exotic types of matter which have been introduced to model acceleratedcosmological expansion go even further and violate the dominant energycondition. This can lead to a cosmological model running into a singularitywhen still expanding 54 . This is known as a ’big rip’ singularity 55 since physicalsystems are ripped apart in finite time as the singularity is approached.The study of these matters is still in a state of flux.Returning to the more conventional setting where the dominant energycondition is satisfied, we can ask what the future holds for the study ofspacetime singularities in classical general relativity. A fundamental fact isthat our understanding is still very incomplete. Two developments promiseimprovements. The first is that the steady increase in computing powerand improvement of numerical techniques means that numerical relativityshould have big contributions to make. The second is that advances in thetheory of hyperbolic partial differential equations are providing the toolsneeded to make further progress with the mathematical theory of solutionsof the Einstein equations. As illustrated by the examples of past successessurveyed in this paper the numerical and mathematical approaches cancomplement each other very effectively.References1. Earman, J. 1995 Bangs, crunches, whimpers and shrieks. Singularities andacausalities in relativistic spacetimes. Oxford University Press, Oxford.2. Penrose, R. 1965 Gravitational collapse and spacetime singularities. Phys.Rev. Lett. 14, 57-59.3. Hawking, S. W. and Ellis, G. F. R. 1973 The large-scale structure of spacetime.Cambridge University Press, Cambridge.4. Penrose, R. 1969 Gravitational collapse: the role of general relativity. Riv.del Nuovo Cimento 1, 252-276.