Abstract
The central dogma of black hole physics — which says that from the outside a black hole can be described in terms of a quantum system with exp(Area/4GN) states evolving unitarily — has recently been supported by computations indicating that the interior of the black hole is encoded in the Hawking radiation of the exterior. In this paper, we probe whether such a dogma for cosmological horizons has any support from similar computations. The fact that the de Sitter bifurcation surface is a minimax surface (instead of a maximin surface) causes problems with this interpretation when trying to import calculations analogous to the AdS case. This suggests anchoring extremal surfaces to the horizon itself, where we formulate a two-sided extremization prescription and find answers consistent with general expectations for a quantum theory of de Sitter space: vanishing total entropy, an entropy of A/4GN when restricting to a single static patch, an entropy of a subregion of the horizon which grows as the region size grows until an island-like transition at half the horizon size when the entanglement wedge becomes the entire static patch interior, and a de Sitter version of the Hartman-Maldacena transition.
Highlights
Has been supported by computations from the gravitational path integral [4, 5], building on [6,7,8,9,10,11]
The central dogma of black hole physics — which says that from the outside a black hole can be described in terms of a quantum system with exp(Area/4GN ) states evolving unitarily — has recently been supported by computations indicating that the interior of the black hole is encoded in the Hawking radiation of the exterior
The fact that the de Sitter bifurcation surface is a minimax surface causes problems with this interpretation when trying to import calculations analogous to the AdS case. This suggests anchoring extremal surfaces to the horizon itself, where we formulate a two-sided extremization prescription and find answers consistent with general expectations for a quantum theory of de Sitter space: vanishing total entropy, an entropy of A/4GN when restricting to a single static patch, an entropy of a subregion of the horizon which grows as the region size grows until an island-like transition at half the horizon size when the entanglement wedge becomes the entire static patch interior, and a de Sitter version of the Hartman-Maldacena transition
Summary
We will use the monotonicity of matter entropy to derive some constraints on the CFT entropy in de Sitter spacetime by conformally mapping to the plane. An annulus in the plane will map to an angular section θ ∈ (θi, θf ) on the spatial sphere of the t = 0 time slice. This is the entropy we want to compute. The sign of κ is fixed by the constraint S0(R) ≥ 0 The latter expression comes from computing the entropy in the complement region, which should factorize into the sum of the entropies of two spheres of radii ρ1 and ρ2, each of which contributes −F. The first derivative decreases from +∞ all the way to zero, by continuity taking all values inbetween
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