Cauchy horizon endpoints and differentiability

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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- Gen.Rel.Grav. 27 93

`Nowhere' differentiable horizons

Piotr T. Chrusciel
(
- Tours U.
)
,
Gregory J. Galloway
(
- Miami U.
)

- Commun.Math.Phys. 193 (1998) 449-470
•
e-Print:
- gr-qc/9611032
•
DOI:
- 10.1007/s002200050336

- Class.Quant.Grav. 9 121

- Proc.Roy.Soc.Lond.A 384 301

Black holes in general relativity

S.W. Hawking
(
- Cambridge U.
)

- Commun.Math.Phys. 25 (1972) 152-166
•
DOI:
- 10.1007/BF01877517

The Chronology protection conjecture

S.W. Hawking
(
- Cambridge U.
)

- Phys.Rev.D 46 (1992) 603-611,
- Boston PASCOS 1991:369-378
•
DOI:
- 10.1103/PhysRevD.46.603

- Gen.Rel.Grav. 16 365

- Int.J.Theor.Phys. 32 137