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The stability of abstract boundary essential singularities

Michael J. S. L. Ashley
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Abstract

The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a chosen family of curves within finite parameter distance. Ashley and Scott proved the first theorem relating essential singularities in strongly causal space-times to causal geodesic incompleteness. Linking this with the work of Beem on the $C^{r}$-stability of geodesic incompleteness allows proof of the stability of these singularities. Here I present this result stating the conditions under which essential singularities are $C^{1}$-stable against perturbations of the metric.

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Michael J. S. L. Ashley. 2002-09-26. The stability of abstract boundary essential singularities. https://arxiv.org/abs/gr-qc/0209098

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