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1. Entanglement phase structure of a holographic BCFT in a black hole background

   https://doi.org/10.1007/JHEP05(2022)153  

   Geng, Hao; Karch, Andreas; Perez-Pardavila, Carlos; Raju, Suvrat; Randall, Lisa; Riojas, Marcos; Shashi, Sanjit (May 2022, Journal of High Energy Physics)

   A<sc>bstract</sc> We compute holographic entanglement entropy for subregions of a BCFT thermal state living on a nongravitating black hole background. The system we consider is doubly holographic and dual to an eternal black string with an embedded Karch-Randall brane that is parameterized by its angle. Entanglement islands are conventionally expected to emerge at late times to preserve unitarity at finite temperature, but recent calculations at zero temperature have shown such islands do not exist when the brane lies below a critical angle. When working at finite temperature in the context of a black string, we find that islands exist even when the brane lies below the critical angle. We note that although these islands exist when they are needed to preserve unitarity, they are restricted to a finite connected region on the brane which we call the atoll. Depending on two parameters — the size of the subregion and the brane angle — the entanglement entropy either remains constant in time or follows a Page curve. We discuss this rich phase structure in the context of bulk reconstruction. 

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2. Information transfer with a gravitating bath

   https://doi.org/10.21468/SciPostPhys.10.5.103  

   Geng, Hao; Karch, Andreas; Perez-Pardavila, Carlos; Raju, Suvrat; Randall, Lisa; Riojas, Marcos; Shashi, Sanjit (January 2021, SciPost Physics)

   Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space. 

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3. Subregion entropy for the doubly-holographic global black string

   Karch, Andreas; Perez-Pardavila, Carlos; Riojas, Marcos; Youssef, Merna (May 2023, The journal of high energy physics)

   a spherical AdS black hole. Compared to previous work, which was limited to the case of planar black holes, this introduces an extra scale to the problem. This allows us to analyze the interplay between the reorganization of entanglement entropy due to island formation and the onset of the Hawking-Page phase transition and to find the appearance of a new critical black hole radius unrelated to the thermodynamics. We also find that the geometry of the Ryu-Takayanagi surface capturing the physics of islands exhibits drastically different behavior than in the planar case. 

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4. Effective entropy of quantum fields coupled with gravity

   https://doi.org/10.1007/JHEP10(2020)052  

   Dong, Xi; Qi, Xiao-Liang; Shangnan, Zhou; Yang, Zhenbin (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe. 

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5. Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

   https://doi.org/10.1088/1361-6382/ac44a0  

   Han, Muxin; Liu, Hongguang (January 2022, Classical and Quantum Gravity)

   Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1 + 1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical HamiltonianH_Δ. The holonomy correction inH_Δis implemented by the $\overline{\mu }$-scheme regularization with a Planckian area scale Δ (which often chosen as the minimal area gap in loop quantum gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g.R_μνρσR^μνρσ∼ 1/Δ². Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry dS₂×S²with Planckian radii $\sim \sqrt{\mathrm{\Delta }}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition. 

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