Abstract
In numerical studies of Gowdy spacetimes evidence has been found for thedevelopment of localized features (`spikes') involvinglarge gradients near the singularity. The rigorousmathematical results available up to now did not coverthis kind of situation. In this work we show theexistence of large classes of Gowdy spacetimesexhibiting features of the kind discovered numerically.These spacetimes are constructed by applying certaintransformations to previously known spacetimes withoutspikes. It is possible to control the behaviour of theKretschmann scalar near the singularity in detail. Thiscurvature invariant is found to blow up in a way which isnon-uniform near the spike in some cases. When thishappens it demonstrates that the spike is a geometricallyinvariant feature and not an artefact of the choice ofvariables used to parametrize the metric. We alsoidentify another class of spikes which are artefacts. Thespikes produced by our method are compared with theresults of numerical and heuristic analyses of the samesituation.
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