Islands in de Sitter space

Abstract

We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal “islands” in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.

Cosmological singularities, entanglement and quantum extremal surfaces

“…We shall describe some relevant details of the behaviour of the extremal surface in the higher dimensional case. In the AdS 5 case, the t(r) function, as a power series solution to (3.17), is 16 3 This is in certain cases consistent with a Euclidean continuation which might lead to a natural initial state (although generic time-dependent spacetimes become complex). For instance de Sitter space ds 2 = R 2 dS τ 2 (−dτ 2 + dx 2 i ) under the analytic continuation τ → ir, R dS → iR AdS becomes Euclidean AdS with corresponding continuations for fields and their boundary conditions; see also e.g.…”

“…Some interesting recent work on quantum extremal surfaces and cosmologies appears in [12,13] and also e.g. [14][15][16][17].…”

Signatures of global symmetry violation in relative entropies and replica wormholes

“…Our argument will give non-trivial results in cases where there is an island in the entanglement wedge of the radiation. The phenomena of islands has been proposed for a variety of scenarios involving different dimensions and also different signs of the cosmological constant (see [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] for some works in this direction and more in a recent review [44]). Our argument is general, but we will use the toy examples in [28] as a concrete set-up for our discussion.…”

Global symmetry, Euclidean gravity, and the black hole information problem

“…In addition to the circumstantial evidence described in the previous paragraph, we can also give a direct argument that, under a set of assumptions we state below, unitary black hole evaporation consistent with the Bekenstein-Hawking formula implies the nonexistence of global symmetries. Our argument makes use of the recent discovery that the "quantum extremal surface" (QES) formula of [12] is powerful enough to compute a unitary Page curve for an evaporating black hole in a wide variety of circumstances [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In this paper we will assume that the basic logic of these calculations applies in any situation where a black hole which is formed quickly evaporates in a unitary manner.…”