Cauchy Horizon Endpoints and Differentiability

Details Cauchy Horizon Endpoints and Differentiability Cauchy Horizon Endpoints and Differentiability

1997-09-18

arxiv.org/abs/gr-qc/9709046v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, Latex

Scientific paper

Cauchy horizons are shown to be differentiable at endpoints where only a single null generator leaves the horizon. A Cauchy horizon fails to have any null generator endpoints on a given open subset iff it is differentiable on the open subset and also iff the horizon is (at least) of class C^1 on the open subset. Given the null convergence condition, a compact horizon which is of class C^2 almost everywhere has no endpoints and is (at least) of class C^1 at all points.

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