Extremal surface barriers. (English) Zbl 1333.83139
Summary: 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. In the context of AdS/CFT, these barriers imply that it is impossible to reconstruct the entire bulk using extremal surfaces. We comment on the implications for the firewall controversy.
MSC:
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 53Z05 | Applications of differential geometry to physics |
Keywords:
gauge-gravity correspondence; AdS-CFT correspondence; classical theories of gravity; spacetime singularitiesReferences:
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