Cauchy Horizon Endpoints and Differentiability

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 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.

16 pages, Latex

References in corpus (1)

• ``Nowhere'' differentiable horizons

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• The crease flow on null hypersurfaces
• Regularity and temperature of stationary black hole event horizons