Cauchy Horizon Endpoints and Differentiability
John K. Beem, Andrzej Krolak
Abstract
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 C1 on the open subset. Given the null convergence condition, a compact horizon which is of class C2 almost everywhere has no endpoints and is (at least) of class C1 at all points.
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