Island Formula from Wald-like Entropy with Backreaction
Shinji Hirano
备注：
20 pages, v2: added references and comments, v3: corrected some remarks, v4: some revisions, added clarifications, comments, and references, the version to appear in JHEP
We propose a Lorentzian derivation of the generalized entropy associated with the island formula for black holes as a Wald-like entropy without reference to the exterior non-gravitating region or field-theoretic von Neumann entropy of Hawking radiation in a fixed curved spacetime background. We illustrate this idea by studying two-dimensional black holes in the Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model in which Hawking radiation is represented by conformal scalars. With some prescriptions assumed, we show that the generalized entropy for the island formula can be reproduced as the Wald-like entropy of the two-dimensional dilaton-gravity theories upon the inclusion of the backreaction from Hawking radiation described by conformal anomaly. We give a discussion on how a similar idea can be applied to higher-dimensional black holes. It is emphasized that the generalized entropy is obtained in a fully gravitational fashion, yet it yields the same Page curve as that of the half-gravitational set-up. We argue that the results in this paper exacerbate the issues raised in the work of massive islands and inconsistency of islands in theories of long-range gravity.
No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (i…
We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries. In the case of weak tension, the brane can be treated as a probe such that its backreaction to the bulk is negligible. We analytically calculate the entanglement entropy of the radiation and obtain the Page curve with the presence of an island on the brane. For the near-extremal black holes, the growth rate is linear in the temperature. Taking both Dvali-Gabadadze-Porrati…
We systematically calculate the quantum extremal surface (QES) associated with Hawking radiation for general $D$-dimensional ($D\geq2$) asymptotically flat (or AdS) eternal black holes using the island formula. We collect the Hawking radiation particles by a non-gravitational bath and find that a QES exists in the near-horizon region outside the black hole when $c\cdot G_{(D)}$ is smaller enough where $c$ is the central charge of the conformal matter and $G_{(D)}$ the $D$-dimensional Newton constant. The locations of the QES in these backgrounds are obtained and the late-time radiation entropy…
We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS$_4$, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black…
We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordström black holes in four dimensions ignoring the backreaction and the greybody factor. Without the island, the entropy of Hawking radiation grows linearly with time, which results in the information paradox for the eternal black holes. By extremizing the generalized entropy that allows the contributions from the island, we find that the island extends to the outside the horizon of the Reissner-Nordström black hole. When taking the effect of the islands into account, it …
We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy. Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture.
Quantum extremal surfaces (QES), codimension-2 spacelike regions which extremize the generalized entropy of a gravity-matter system, play a key role in the study of the black hole information problem. The thermodynamics of QESs, however, has been largely unexplored, as a proper interpretation requires a detailed understanding of backreaction due to quantum fields. We investigate this problem in semi-classical Jackiw-Teitelboim (JT) gravity, where the spacetime is the eternal two-dimensional Anti-de Sitter ($\text{AdS}_{2}$) black hole, Hawking radiation is described by a conformal field theory…
A classical thought-experiment to destroy black holes was envisaged by Wald in 1974: it consists of throwing particles with large angular momentum into an extremal black hole, checking whether their capture can over-spin the black hole past the extremal limit and create a naked singularity. Wald showed that in the test-particle limit, particles that would be otherwise capable of producing naked singularities are simply scattered. Recently Jacobson and Sotiriou showed that if one considers instead a black hole that is almost, but not exactly extremal, then in the absence of backreaction effects…
Black Hole Interior and Quantum Error Correction with Dynamical Gravity
Center for Gravitational Physics and Quantum Information (CGPQI), Yukawa Institute for Theoretical Physics (YITP), Kyoto University（京都大学引力物理与量子信息中心（CGPQI），理论物理汤川研究所（YITP））；Department of Physics, Rikkyo University（立教大学物理系）
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