Entanglement between two evaporating black holes

Miyata, Akihiro; Ugajin, Tomonori

doi:10.1007/jhep09(2022)009

“…From the aspect of path integral formalism, the emergence of islands corresponds to the dominance of another saddle point, known as the wormhole saddle point, where Euclidean wormholes connect the different replicas [56,57] (See also [58,59]). Inspired by this thought-provoking viewpoint, the notion of "wormhole" was extensively discussed as the bridge between disjoint universes [60][61][62][63][64], where the wormhole behind horizons is lengthened, as well as in baby universes [65][66][67][68], which connect to parent universes through a wormhole.…”

Section: Introductionmentioning

confidence: 99%

Black holes entangled by radiation

Liu

¹

,

Xian

²

,

Peng

³

et al. 2022

J. High Energ. Phys.

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We construct three models to describe the scenario where two eternal black holes are separated by a flat space, and can eventually be entangled by exchanging radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the black holes are not equal, we observe a loss of entanglement between the smaller black hole and the radiation at late times. On the field theory side, we consider two Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble two black holes connected by a radiation region. We numerically compute the same entanglement measures and obtain similar phase structures as the bulk results. In general, a time delay of the entanglement between the SYK clusters is found in cases with a long Majorana chain. In particular, when the SYK clusters are different in size, similar entanglement loss between the smaller SYK cluster and the Majorana chain is observed. Finally, we investigate a chain model composed of EPR clusters with particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.

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“…The reason why it is even possible to apply the derived expressions for the entropy to de Sitter space is that they are agnostic about the precise background under consideration. While originally studied in the context of holography in Anti-de Sitter space, JHEP01(2023)129 by now many works have applied this so-called island formula to other backgrounds, such as a plethora of black hole solutions [16][17][18][19][20][21][22][23][24][25] and cosmological spacetimes [14,15,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. As long as it is possible to unambiguously define a subsystem entangled with a gravitating region, the island formula applies.…”

Section: Introductionmentioning

confidence: 99%

An outsider’s perspective on information recovery in de Sitter space

Aalsma

¹

,

Aguilar-Gutierrez

²

,

Sybesma

³

2023

J. High Energ. Phys.

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Entanglement islands play a crucial role in our understanding of how Hawking radiation encodes information in a black hole, but their relevance in cosmological spacetimes is less clear. In this paper, we continue our investigation of information recovery in de Sitter space and construct a two-dimensional model of gravity containing a domain wall that interpolates between de Sitter space and Rindler space. The Rindler wedges introduce weakly-gravitating asymptotic regions from which de Sitter space can be probed, yielding an outside perspective of the cosmological horizon. In contrast to earlier works, backreaction effects are under control by considering a quantum state that only breaks the thermal equilibrium of the Bunch-Davies state for a finite time. This allows information to be decoded from the Gibbons-Hawking radiation in a controlled fashion.

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De Sitter space is sometimes not empty

Balasubramanian,

Nomura,

Ugajin

2024

J. High Energ. Phys.

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Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity — novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon $$ \left({S}_{\textrm{dS}}={A}_{\textrm{horizon}}^{\textrm{dS}}/4{G}_{\textrm{N}}\right) $$ S dS = A horizon dS / 4 G N is less than the entropy of the AdS black hole horizon $$ \left({S}_{\textrm{BH}}={A}_{\textrm{horizon}}^{\textrm{AdS}}/4{G}_{\textrm{N}}\right) $$ S BH = A horizon AdS / 4 G N , i.e., SdS< SBH; (c) the entanglement entropy is finite when SdS > SBH. Thus, the de Sitter Hilbert space is effectively nontrivial only when SdS > SBH. The AdS black hole we introduce can be regarded as an “observer” for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

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Entanglement between two evaporating black holes

Cited by 7 publications

References 78 publications

Black holes entangled by radiation

Black holes entangled by radiation

An outsider’s perspective on information recovery in de Sitter space

De Sitter space is sometimes not empty

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