The stability of abstract boundary essential singularities

Details The stability of abstract boundary essential singularities The stability of abstract boundary essential singularities

2002-09-26

arxiv.org/abs/gr-qc/0209098v1

Gen.Rel.Grav. 34 (2002) 1625-1635

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

to appear in GRG October 2002 - contains tex source and 2 ps figures

Scientific paper

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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