Manufacture of Gowdy spacetimes with spikes

TL;DR

This paper constructs and analyzes Gowdy spacetimes with localized spike features near singularities, demonstrating their geometric invariance and providing detailed control over curvature behavior.

Contribution

It introduces a method to generate Gowdy spacetimes with spikes, showing their geometric invariance and detailed curvature behavior near singularities.

Findings

Spikes can be constructed explicitly in Gowdy spacetimes.

Spikes can be geometrically invariant features, not just coordinate artifacts.

Curvature invariants like the Kretschmann scalar can blow up non-uniformly near spikes.

Abstract

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.