Built on

S. W. Hawking, “Gravitational radiation from colliding black holes,” Phys. Rev. Lett. 26
1971
Earlier work this paper cites.
P. Háj́ic̃ek, “Exact Models of Charged Black Holes. I. Geometry of Totally Geodesic Null Hypersurface”, Commun. Math. Phys. 34
1973
Earlier work this paper cites.
S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Spacetime,” Cambridge University Press, Cambridge, 1973
1973
Earlier work this paper cites.
R. Schoen and L. Simon, “Regularity of stable minimal hypersurfaces,” Comm. Pure. Appl. Math
1981
Earlier work this paper cites.
W. W. Meeks, III and S. T. Yau, “The existence of embedded minimal surfaces and the problem of uniqueness,” Math. Z
1982
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
J. M. Maldacena, “Wilson loops in large N field theories,” Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
J. Louko, D. Marolf and S. F. Ross, Phys. Rev. D 62
2000
Earlier work this paper cites.
P. Kraus, H. Ooguri and S. Shenker, “Inside the horizon with AdS / CFT,” Phys. Rev. D 67
2003
Earlier work this paper cites.
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, “The Black hole singularity in AdS / CFT,” JHEP 0402
2004
Earlier work this paper cites.
T. Hertog and G. T. Horowitz, JHEP 0407
2004
Earlier work this paper cites.

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2013

Extremal Surface Barriers

Engelhardt, Netta, Wall, Aron C.

Understand

We present a generic condition for Lorentzian manifolds to have a barrier that limits the reach of boundary-anchored extremal surfaces of arbitrary dimension.

We show that any surface with nonpositive extrinsic curvature is a barrier, in the sense that extremal surfaces cannot be continuously deformed past it.
Furthermore, the outermost barrier surface has nonnegative extrinsic curvature.
Under certain conditions, we show that the existence of trapped surfaces implies a barrier, and conversely.

Built on

S. W. Hawking, “Gravitational radiation from colliding black holes,” Phys. Rev. Lett. 26
1971
Earlier work this paper cites.
P. Háj́ic̃ek, “Exact Models of Charged Black Holes. I. Geometry of Totally Geodesic Null Hypersurface”, Commun. Math. Phys. 34
1973
Earlier work this paper cites.
S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Spacetime,” Cambridge University Press, Cambridge, 1973
1973
Earlier work this paper cites.
R. Schoen and L. Simon, “Regularity of stable minimal hypersurfaces,” Comm. Pure. Appl. Math
1981
Earlier work this paper cites.
W. W. Meeks, III and S. T. Yau, “The existence of embedded minimal surfaces and the problem of uniqueness,” Math. Z
1982
Earlier work this paper cites.
J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
J. M. Maldacena, “Wilson loops in large N field theories,” Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
J. Louko, D. Marolf and S. F. Ross, Phys. Rev. D 62
2000
Earlier work this paper cites.
P. Kraus, H. Ooguri and S. Shenker, “Inside the horizon with AdS / CFT,” Phys. Rev. D 67
2003
Earlier work this paper cites.
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, “The Black hole singularity in AdS / CFT,” JHEP 0402
2004
Earlier work this paper cites.
T. Hertog and G. T. Horowitz, JHEP 0407
2004
Earlier work this paper cites.