Island and Page curve for one-sided asymptotically flat black hole

We study an evaporating black hole in the boundary conformal field theory (BCFT) model under the fully time-dependent AdS-Vaidya spacetime geometry. We introduce the time-dependent finite bath termed the effective Hawking radiation region. This is described by a nontrivial BCFT solution that acts as a time-dependent brane which we call the moving end-of-the-radiation (METR) brane that leads to a new type of Hubeny-Rangamani-Takayanagi surface. We further examine the island formulation in this particular time-dependent spacetime. The Page curve is calculated by using Holographic Entanglement Entropy (HEE) in the context of double holography.

Section: Motivation and Discussionmentioning

confidence: 99%

“…To date, most works on the information problem for dimensions d ≥ 3 have been focused on eternal black holes [21,36,46,75,85,[103][104][105][106]. In addition, even though the model in [108] has considered some element of dynamical evolution on the brane, the bulk is still essentially a static spacetime.…”

Section: Evaporating Black Holementioning

confidence: 99%

Page curve of AdS-Vaidya model for evaporating black holes

Chou,

Lao,

Yang

2024

“…Also, the analytical answer for entanglement entropy of matter is known only in some special models, including two-dimensional conformal field theory [38][39][40]. More complicated setups, such as higher-dimensional spacetimes or spacetimes with no asymptotically flat subregions, are still subjects of research [31,34,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. As for de Sitter, the literature uses a specific setup, in which the original manifold is either initially two-dimensional or is reduced to two dimensions, and the applicability of the island formula is postulated [42,45,[58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy in de Sitter: no pure states for conformal matter

Ageev,

Aref’eva,

Belokon

et al. 2024

In this paper, we consider the entanglement entropy of conformal matter for finite and semi-infinite entangling regions, as well as the formation of entanglement islands in four-dimensional de Sitter spacetime partially reduced to two dimensions. We analyze complementarity and pure state condition of entanglement entropy of pure states as a consistency test of the CFT formulas in this geometrical setup, which has been previously used in the literature to study the information paradox in higher-dimensional de Sitter in the context of the island proposal. We consider two different types of Cauchy surfaces in the extended static patch and flat coordinates, correspondingly. For former, we found that entanglement entropy of a pure state is always bounded from below by a constant and never becomes zero, as required by quantum mechanics. In turn, the difference between the entropies for some region and its complement, which should be zero for a pure state, in direct calculations essentially depends on how the boundaries of these regions evolve with time. Regarding the flat coordinates, it is impossible to regularize spacelike infinity in a way that would be compatible with complementarity and pure state condition, as opposed, for instance, to two-sided Schwarzschild black hole. Finally, we discuss the information paradox in de Sitter and show that the island formula does not resolve it, at least in this setup. Namely, we give examples of a region with a time-limited growth of entanglement entropy, for which there is no island solution, and the region, for which entanglement entropy does not grow, but the island solution exists.

Geometrizing the partial entanglement entropy: from PEE threads to bit threads

Lin,

Lu,

Wen

2024

We give a scheme to geometrize the partial entanglement entropy (PEE) for holographic CFT in the context of AdS/CFT. More explicitly, given a point x we geometrize the two-point PEEs between x and any other points in terms of the bulk geodesics connecting these two points. We refer to these geodesics as the PEE threads, which can be naturally regarded as the integral curves of a divergenceless vector field $$ {V}_{\textbf{x}}^{\mu } $$ V x μ , which we call PEE thread flow. The norm of $$ {V}_{\textbf{x}}^{\mu } $$ V x μ that characterizes the density of the PEE threads can be determined by some physical requirements of the PEE. We show that, for any static interval or spherical region A, a unique bit thread configuration can be generated from the PEE thread configuration determined by the state. Hence, the non-intrinsic bit threads are emergent from the intrinsic PEE threads. For static disconnected intervals, the vector fields describing a divergenceless flow is no longer suitable to reproduce the RT formula. We weight a PEE thread with the number of times it intersects with any homologous surface. Instead, the RT formula is perfectly reformulated by the minimization of the summation of PEE threads with all possible assignment of weights.