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The Geroch/Stephani transformation is a solution-generating transformation,and may generate spiky solutions. The spikes in solutions generated so far areeither early-time permanent spikes or transient spikes. We want to generate asolution with a late-time permanent spike. We achieve this by applying theStephani transformation with the rotational Killing vector field of the locallyrotationally symmetric Jacobs solution. The late-time permanent spike occursalong the cylindrical axis. The generated solution also features a rich varietyof transient structures. We introduce a new technique to analyse thesestructures. Our findings lead us to discover a transient behaviour, which wecall the overshoot transition.

Generating spiky solutions of Einstein field equations with the Stephani transformation