Abstract
We prove that consistency of the holographic dictionary implies a hallmark prediction of the weak cosmic censorship conjecture: that in classical gravity, trapped surfaces lie behind event horizons. In particular, the existence of a trapped surface implies the existence of an event horizon, and that furthermore this event horizon must be outside of the trapped surface. More precisely, we show that the formation of event horizons outside of a strong gravity region is a direct consequence of causal wedge inclusion, which is required by entanglement wedge reconstruction. We make few assumptions beyond the absence of evaporating singularities in strictly classical gravity. We comment on the implication that spacetimes with naked trapped surfaces do not admit a holographic dual, note a possible application to holographic complexity, and speculate on the dual CFT interpretation of a trapped surface.
Highlights
JHEP07(2021)066 forbids the existence of trapped surfaces — i.e. surfaces from which light rays converge in any direction due to gravitational lensing — outside of event horizons [25]
We prove that consistency of the holographic dictionary implies a hallmark prediction of the weak cosmic censorship conjecture: that in classical gravity, trapped surfaces lie behind event horizons
Since by step one there are no timelike curves from the Hubeny-Rangamani-Takayanagi [38] (HRT) surface to I, there can be no future-directed timelike curves from the apparent horizon to I : we find that apparent horizons must lie outside of I−[I ] in the coarse-grained spacetime; under the assumption that singularities do not evaporate in classical spacetimes satisfying the null energy condition, we can deduce that apparent horizons must lie behind the event horizon in the original spacetime
Summary
Assumptions: we will assume the null convergence condition, Rabkakb ≥ 0 for all null vectors ka as well as the HRT prescription for computing SvN (1.1) and entanglement wedge reconstruction. If the CFT evolution is well-defined (for N → ∞) only between two (potentially empty) boundary time slices C− and C+ of the maximal conformal extension (∂M, h), C+ being to the future of C−, we excise J+[C+] and J−[C−] from (M, g). This is because these regions are not encoded in the CFT state between C− and C+, and so the spacetime without the excision is not completely encoded in the CFT and not holographic..
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