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8.4 Cosmic censorship in Gowdy spacetimes

In as yet unpublished work Ringström has proved strong cosmic censorship for Gowdy spacetimes with the spatial topology of a torus, thus completing a quest which has been going on for twenty-five years. Since it was shown in [316] that these spacetimes are geodesically complete in the future, proving strong cosmic censorship comes down to showing that for generic initial data the corresponding maximal Cauchy development is inextendible towards the past. The method for doing this is to prove enough about the asymptotics near the singularity to show that the Kretschmann scalar blows up along past incomplete causal geodesics.

With a suitable genericity assumption (restriction to an open dense set of initial data) it is shown that the singularity has a structure which is similar to that found in the solutions constructed in [310]. An important technical tool is to show the existence of an ‘asymptotic velocity’. This is a function constructed out of a given solution which allows the identification of the points at which localized spatial structure in the sense of Section 8.3 is formed.


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