Treating Maxwell soft hair as a transition function that relates U(1) gauge fields living in the asymptotic region and near-horizon region, the U(1) gauge parameter $ϕ$ naturally becomes a good label of those Maxwell soft hair degrees of freedom. This interpretation also builds the connection between Maxwell soft hair and U(1) edge modes living in the intermediate region, which admits a well-defined effective action description. We study the statistical properties by Euclidean path integral, which concludes that the soft hair density of state increases with black hole temperature. Hawking radiations increase black hole entropy by creating entanglements, while the measurements of soft modes project the black hole onto lower entropy states. The competition between phase spaces of Hawking radiations and soft hair measurements gives rise to one version of the Page curve consistent with the unitary evolution of the black hole.
We argue that the semiclassical analysis of the black hole information paradox is incomplete and has to be completed by an explicit entanglement of matter and quantum gravity degrees of freedom. We study in detail the evaporation process from beginning to end in the light of our extension and show that a pure initial state remains pure over the full evaporation process, including the final state which remains after the black hole has completely evaporated. By the same token we show how the quantum hair is encoded in the micro structure of the (final) gravitational state which is entangled with…
We present a paradox for evaporating black holes, which is common in most schemes trying to avoid the firewall by decoupling early and late radiation. At the late stage of the black hole evaporation, the decoupling between early and late radiation can not be realized because the black hole has a very small coarse-grained entropy, then we are faced with the firewall again. We call the problem hair-loss paradox as a pun on losing black hole soft hair during the black hole evaporation and the situation that the information paradox has put so much pressure on researchers.
We propose a model with multiple qubits that reproduces the thermal properties of 4-dimensional (4-dim) Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft hair evaporation at horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair, and that late Hawking radiation can be highly e…
In the context of black hole chemistry, we study the thermodynamics of asymptotically de Sitter black holes with conformal scalar hair in Einstein gravity. The hair parameter allows us to attain thermodynamic equilibrium between the event horizon and the cosmological horizon. We find that the system of the black hole and the de Sitter space surrounding it undergo a Reverse Hawking-Page phase transition provided we consider the grand-canonical ensemble.
Page curve for the fine grained entropy of the black hole radiation is obtained once we include the effect of a non vanishing quantum Fisher information in the evaporation data. This quantum Fisher information scales as the inverse of the original black hole entropy. The modified fine grained entropy can be naturally related to a relative entanglement entropy with the quantum Fisher information defining the curvature at Page point.
Asymptotic Causal Diamonds (ACDs) are a natural flat space analogue of AdS causal wedges, and it has been argued previously that they may be useful for understanding bulk locality in flat space holography. In this paper, we use ACD-inspired ideas to argue that there exist natural candidates for Quantum Extremal Surfaces (QES) and entanglement wedges in flat space, anchored to the conformal boundary. When there is a holographic screen at finite radius, we can also associate entanglement wedges and entropies to screen sub-regions, with the system naturally coupled to a sink. The screen and the b…
In an ordinary quantum field theory, the "split property" implies that the state of the system can be specified independently on a bounded subregion of a Cauchy slice and its complement. This property does not hold for theories of gravity, where observables near the boundary of the Cauchy slice uniquely fix the state on the entire slice. The original formulation of the information paradox explicitly assumed the split property and we follow this assumption to isolate the precise error in Hawking's argument. A similar assumption also underpins the monogamy paradox of Mathur and AMPS. Finally the…
A recent, intriguing paper by Hawking, Perry and Strominger suggests that soft photons and gravitons can be regarded as black hole hair and may be relevant to the black hole information paradox. In this note we make use of factorization theorems for infrared divergences of the S-matrix to argue that by appropriately dressing in and out hard states, the soft-quanta-dependent part of the S-matrix becomes essentially trivial. The information paradox can be fully formulated in terms of dressed hard states, which do not depend on soft quanta.
It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.
The information loss paradox remains unresolved ever since Hawking's seminal discovery of black hole evaporation. In this essay, we revisit the entanglement entropy via Euclidean path integral (EPI) and allow for the branching of semi-classical histories during the Lorentzian evolution. We posit that there exist two histories that contribute to EPI, where one is information-losing that dominates at early times, while the other is information-preserving that dominates at late times. By so doing we recover the Page curve and preserve the unitarity, albeit with the Page time shifted significantly…
We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild-AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawk…
One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the b…
Hawking, Perry and Strominger recently invoked BMS symmetry charges in an attempt to resolve the black hole information paradox. Here we propose an alternative scenario that is based on the Kac-Moody charges. We show that the role of BMS charges can be played by an infinite set of symmetries that emerge from the space-time foam predicted by quantum gravity. Specifically, we focus on Yang-Mills fields embedded in the gravity described by the Holst formulation, and argue that the Yang-Mills and gravitational self-duality conditions in space-time bubbles are related to a new infinite dimensional …
By using the quantum extremal island formula, we perform a simple calculation of the generalized entanglement entropy of Hawking radiation from the two dimensional Liouville black hole. No reasonable island was found when extremizing the generalized entropy. We explain qualitatively the reason why the page curve cannot be reproduced in the present model. This suggests that the islands may not necessarily save the information paradox for the Liouville black holes.
Introducing a new form of scalar potential $V(ϕ)$, we derive a proper form of the rotating black hole solution in three-dimensional Einstein gravity with nonminimally coupled scalar field and find that the first law of thermodynamics of this new rotating hairy black hole can be protected, where the scalar field parameter $B$ is constrained to relate to the black hole size. We also disclose the Hawking-Page phase transition between this rotating hairy black holes and the pure thermal radiation. Moreover, we study phase transitions between this rotating hairy black hole and rotating BTZ black ho…
A rotating hairy black hole solution is found in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. Then we discuss analytically the horizon structure and find an analogue of the famous Kerr bound in (2+1) dimensions because of the existence of black hole horizons. We present the asymptotic symmetries and find the same symmetry group (i.e. the conformal group) and central charge as in pure gravity. Based on the asymptotic behavior, the mass and angular momentum are presented by the Regge-Teitelboim approach. Other thermodynamic quantities are also …
In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in…
We consider large gauge transformations of gravity and electromagnetism in D=4 asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large U(1) charge conservation. Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge s…
The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry and Strominger's proposal for supertranslations to provide a solution to …
We consider a thought experiment in which an energetic massless string probes a "stringhole" (a heavy string lying on the correspondence curve between strings and black holes) at large enough impact parameter for the regime to be under theoretical control. The corresponding, explicitly unitary, $S$-matrix turns out to be perturbatively sensitive to the microstate of the stringhole: in particular, at leading order in $l_s/b$, it depends on a projection of the stringhole's Lorentz-contracted quadrupole moment. The string-black hole correspondence is therefore violated if one assumes quantum hair…
The black hole singularity plays a crucial role in formulating Hawking's information paradox. The global spacetime analysis may be reconciled with unitarity by imposing a final state boundary condition on the spacelike singularity. Motivated by the final state proposal, we explore the effect of final state projection in two dimensional conformal field theories. We calculate the time evolution under postselection by employing the real part of pseudo-entropy to estimate the amount of quantum entanglement averaged over histories between the initial and final states. We find that this quantity pos…
We use an argument by Page to exhibit a paradox in the global description of the multiverse: the overwhelming majority of observers arise from quantum fluctuations and not by conventional evolution. Unless we are extremely atypical, this contradicts observation. The paradox does not arise in the local description of the multiverse, but similar arguments yield interesting constraints on the maximum lifetime of metastable vacua.
It is known that there is no three-dimensional analog of de Sitter black holes. I show that the analog does exist when non-Gaussian (i.e., ring-type) smearings of point matter hairs are considered. This provides a new way of constructing black hole solutions from hairs. I find that the obtained black hole solutions are quite different from the usual large black holes in that there are i) large to small black hole transitions which may be considered as inverse Hawking-Page transitions and ii) soliton-like (i.e., non-perturbative) behaviors. For Gaussian smearing, there is no black hole but a gr…
We argue that a convenient way to analyze instabilities of black holes in AdS space is via Bragg-Williams construction of a free energy function. Starting with a pedagogical review of this construction in condensed matter systems and also its implementation to Hawking-Page transition, we study instabilities associated with hairy black holes and also with the $R$-charged black holes. For the hairy black holes, an analysis of thermal quench is presented.
Parikh and Wilczek formulated Hawking radiation as quantum tunneling across the event horizon proving the spectrum to be nonthermal. These nonthermality factors emerging due to back reaction effects have been claimed to be responsible for correlations among the emitted quanta. It has been proposed by several authors in literature that these correlations actually carry out information locked in a black hole and hence provide a resolution to the long debated black hole information paradox. This paper demonstrates that this is a fallacious proposition. Finally, it formulates the implications of t…
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 present a doubly holographic prescription for computing entanglement entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a Dirichlet anchoring condition. In braneworld cosmology, a related approach was used previously in arXiv:2007.06551. There, the prescription naturally computed a co-moving entanglement entropy, and was argued to resolve the information paradox for a black hole living in the cosmology. In this paper, we show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath.…
When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time $β/2π\log S_{BH}$ into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decrea…
In this paper, we have analyzed the information paradox and its resolution using island proposal in Schwarzschild de-Sitter black hole spacetime. First, we study the information paradox for the black hole patch by treating de-Sitter patch on both sides as a frozen background (by inserting thermal opaque membrane) and then we carry out similar study for de-Sitter patch also. In both cases, when there is no island surface then the entanglement entropy has as usual the linear time dependence whereas in the presence of an island surface entanglement entropy become constant (equal to twice of therm…
In this short note using the analogy with the recent resolution of the black hole information paradox we conjecture the order parameter for the state of consciousness based on the notion of the Page curve and the Page time. The entanglement between the state of the brain and time series of neuronal firing as well as the non-orthogonality of the functional connectomes play a key role.
We review recent progress on the information paradox. We explain why exponentially small correlations in the radiation emitted by a black hole are sufficient to resolve the original paradox put forward by Hawking. We then describe a refinement of the paradox that makes essential reference to the black-hole interior. This analysis leads to a broadly-applicable physical principle: in a theory of quantum gravity, a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This principle can be made precise and established -- under weak assumptions, and using …
The black hole information problem has been a challenge since Hawking's original 1975 paper. It led to the discovery of AdS/CFT, which gave a partial resolution of the paradox. However, recent developments, in particular the firewall puzzle, show that there is much that we do not understand. I review the black hole, Hawking radiation, and the Page curve, and the classic form of the paradox. I discuss AdS/CFT as a partial resolution. I then discuss black hole complementarity and its limitations, leading to many proposals for different kinds of `drama.' I conclude with some recent ideas.
One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S-matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile tha…
In the spirit of studying the information paradox as a scattering problem, we pose and answer the following questions: i) What is the scattering amplitude for $N$ particles to emerge from a large black hole when two energetic particles are thrown into it? ii) How long would we have to wait to recover the information sent in? The answer to the second question has long been expected to be Page time, a quantity associated with the lifetime of the black hole. We answer the first by evaluating an infinite number of `ladder of ladders' Feynman diagrams to all orders in $M_{Pl}/M_{BH}$. Such processe…
Page transition for the complexity of an evaporating black hole
University of California, Berkeley（加州大学伯克利分校）；Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理与物理系）；Theoretical Physics Group, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室理论物理组）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo（东京大学宇宙物理学与数学 Kavli 研究所（WPI））；Sandia National Laboratories（桑迪亚国家实验室）
In theories with a perturbatively massless 2-form (dual to an axion), a paradox may arise in the process of black hole evaporation. Schwarzschild black holes can support a non-trivial Wilson-line-type field, the integral of the 2-form around their horizon. After such an 'axionic black hole' evaporates, the Wilson line must be supported by the corresponding 3-form field strength in the region formerly occupied by the black hole. In the limit of small axion decay-constant f, the energy required for this field configuration is too large. The natural resolution is through the presence of light str…
We review some recent results obtained for black holes using effective field theory methods applied to quantum gravity, in particular the unique effective action. Black holes are complex thermodynamical objects that not only have a temperature but also have a pressure. Furthermore, they have quantum hair which provides a solution to the black hole information paradox.
Recent results on the infrared structure of gravity and electromagnetism have suggested that the deep infrared is much richer than previously appreciated. This article presents a generalisation of these findings within the context of abelian and nonabelian soft (i.e. zero-energy) gauge charges. As a warm up, we describe the emergence of an infinity of soft magnetic charges even in the absence of magnetic monopoles. We show that two infinite sets of soft charges arise in the nonabelian theory as well. In light of the concomitant conservation laws associated with the soft charges, we revisit the…
We formulate a version of the information paradox in de Sitter spacetime and show that it is solved by the emergence of entanglement islands in the context of the DS/dS correspondence; in particular, the entanglement entropy of a subregion obeys a time-dependent Page curve. Our construction works in general spacetime dimensions and keeps the graviton massless. We interpret the resulting behavior of the entanglement entropy using double holography. It suggests that the spatial distribution of microscopic degrees of freedom depends on descriptions, as in the case of a black hole. In the static (…
