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According to black hole complementarity, for an external observer, the interior of the black hole is replaced with a stretched horizon at a Planck distance above where the horizon ought to be. Is this stretched horizon an end-of-space boundary with a Gibbons-York term, or does it have an interior a la fuzzball complementarity? Is fuzzball complementarity different because it has an interior according to external observers?

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Maybe you are interested in what says about fuzzballs and firewalls here. – Dilaton Dec 3 '12 at 12:35

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If a stretched horizon is really an end to space and hovering a Planck length above where the horizon ought to be, then if you have bothered to work out the details, you should have known that its principal eigenvalue extrinsic curvature in the timelike direction goes as $l_P^{-1}$ while its principal eigenvalue extrinsic curvature along the angular directions goes as $l_P/R^2$. This is incompatible with a Gibbons-York term, which requires both to be the negative of each other but equal in magnitude.

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