MSc. thesis submitted to ODTU. Table of contents entries referring to subsections of the index are added (The only addition to the library version). v2: more comprehensive, visually attractive v3: Published as a book by LAP LAMBERT Academic Publishing (December 20, 2016)
In this MSc. thesis, we have attempted to give an overview of the firewall paradox and various approaches towards its resolution. After an introductory chapter on some basic concepts in quantum field theory in curved spacetimes such as Hawking radiation, we introduce the paradox. It arises out of application of principles each of which is thought or assumed to be correct: 1) unitary black hole evaporation, 2) validity of quantum field theory in curved spacetime, 3) a measure of the number of black hole quantum states, 4) Einstein's equivalence principle. Then, we present various approaches that exist in the literature towards the resolution of the paradox.
Almheiri, Marolf, Polchinski, and Sully argued that, for a consistent black hole evaporation process, the horizon of a sufficiently old black hole should be replaced by a "firewall" at which an infalling observer burns up, which obviously leads to the violation of the equivalence principle. We propose that once the infalling partner of an outgoing Hawking particle approaches a black hole singularity, it experiences decoherence and the loss of its entanglement with the outgoing Hawking particle. This implies we would no longer need firewalls to avoid the black hole information paradox.
Unitary evolution makes pure state on one Cauchy surface evolve to pure state on another Cauchy surface. Outgoing Hawking radiation is only subsystem on the late Cauchy surface. The requirement that Hawking radiation to be pure amounts to require purity of subsystem when total system is pure. We will see this requirement will lead to firewall even in \textit{flat} spacetime, and thus is invalid. Information is either stored in the entanglement between field modes inside black hole and the outgoing modes or stored in correlation between geometry and Hawking radiation when singularity is resolve…
The firewall paradox for black holes is often viewed as indicating a conflict between unitarity and the equivalence principle. We elucidate how the paradox manifests as a limitation of semiclassical theory, rather than presents a conflict between fundamental principles. Two principal features of the fundamental and semiclassical theories address two versions of the paradox: the entanglement and typicality arguments. First, the physical Hilbert space describing excitations on a fixed black hole background in the semiclassical theory is exponentially smaller than the number of physical states in…
Despite being a major component in the teaching of special relativity, the twin `paradox' is generally not examined in courses on general relativity. Due to the complexity of analytical solutions to the problem, the paradox is often neglected entirely, and students are left with an incomplete understanding of the relativistic behaviour of time. This article outlines a project, undertaken by undergraduate physics students at the University of Sydney, in which a novel computational method was derived in order to predict the time experienced by a twin following a number of paths between two given…
Acoustic Firewalls: Analogue Gravity Perspective on the AMPS Paradox
Nantong University（南通大学）；Kuban State University（库班国立大学）；Joint-Stock Company “Center for Research and Development”（联合股份公司“研究与发展中心”）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）
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 consider the information loss paradox at different angles, from the standard semi-classical approximation of General Relativity to the recently proposed scenarios of black holes evolution caused by effects of gravity quantization. Focusing on the Firewall proposal, we study the loop effects on the geometry and boundary conditions in black hole spacetimes and analyze the energy measured by an infalling observer near their horizons. As a result we obtain a trans-Planckian energy transition for the time-dependent black hole solution on the quantum-induced AdS background, the importance of whic…
Interest in the black hole information paradox has recently been catalyzed by the newer "firewall" argument. The crux of the updated argument is that previous solutions which relied on observer complementarity are in violation of the quantum condition of monogamy of entanglement; with the prescribed remedy being to discard the equivalence principle in favor of an energy barrier (or firewall) at the black hole horizon. Differing points of view have been put forward, including the "ER=EPR" counterargument and the final-state solution, both of which can be viewed as potential resolutions to the a…
Black holes offer an exciting area to explore the nature of quantum gravity. The classic work on Hawking radiation indicates that black holes should decay via quantum effects, but our ideas about how this might work at a technical level are incomplete. Recently Almheiri-Marolf-Polchinski-Sully (AMPS) have noted an apparent paradox in reconciling fundamental properties of quantum mechanics with standard beliefs about black holes. One way to resolve the paradox is to postulate the existence of a "firewall" inside the black hole horizon which prevents objects from falling smoothly toward the sing…
We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the g…
The black hole information loss paradox has long been one of the most studied and fascinating aspects of black hole physics. In its latest incarnation, it takes the form of the firewall paradox. In this paper, we first give a conceptually oriented presentation of the paradox, based on the notion of causal structure. We then suggest a possible strategy for its resolutions and see that the core idea behind it is that there are connections that are non-local for semiclassical physics, which have to be taken into account when studying black holes. We see how to concretely implement this strategy i…
I distinguish between two versions of the black hole information-loss paradox. The first arises from apparent failure of unitarity on the spacetime of a completely evaporating black hole, which appears to be non-globally-hyperbolic; this is the most commonly discussed version of the paradox in the foundational and semipopular literature, and the case for calling it `paradoxical' is less than compelling. But the second arises from a clash between a fully-statistical-mechanical interpretation of black hole evaporation and the quantum-field-theoretic description used in derivations of the Hawking…
One of the most fundamental features of a black hole in general relativity is its event horizon: a boundary from which nothing can escape. There has been a recent surge of interest in the nature of these event horizons and their local neighbourhoods. In an attempt to resolve black hole information paradox(es), and more generally, to better understand the path towards quantum gravity, "firewalls" have been proposed as an alternative to black hole event horizons. In this paper, we explore the phenomenological implications of black holes possessing a surface or "firewall", and predict a potential…
Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler-deWitt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom. The "firewall" argument that unitarity of black hole S-matrix implies the presence of a highly excited quantum state near the horizon is based on such a factorization, hence is not applicable in…
In this thesis, we have studied the information loss paradox in detail. As a first step, we have derived the main results of quantum field theory in a curved background. We have discussed the case of the free scalar Klein-Gordon field and concluded with a derivation of the so-called Unruh effect in Minkowski spacetime. After giving a brief survey of necessary concepts, such as surface gravity and the redshift factor, we have applied them along the results from the Unruh effect to derive the temperature of Hawking radiation. Later, we have used the formalism of QFT in curved spacetime to rigoro…
The black hole information paradox and the black hole entropy are currently extensively researched. The consensus about the solution of the information paradox is not yet reached, and it is not yet clear what can we learn about quantum gravity from these and the related research. It seems that the apparently irreducible paradoxes force us to give up on at least one well-established principle or another. Since we are talking about a choice between the principle of equivalence from general relativity, and some essential principles from quantum theory, both being the most reliable theories we hav…
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.
We argue that the resolution to the black hole information paradox lies in a proper accounting of the implications of diffeomorphism invariance for the Hilbert space and observables of quantum gravity. The setting of asymptotically Anti-de Sitter spacetime is adopted for most of the paper, but in the framework of canonical quantum gravity, without invoking AdS/CFT duality. We present Marolf's argument that boundary unitarity is a consequence of diffeomorphism invariance, and show that its failure to apply in the classical limit results from a lack of analyticity that has no quantum counterpart…
We review a recently proposed effective Tolman temperature and present its applications to various gravitational systems. In the Unruh state for the evaporating black holes, the free-fall energy density is found to be negative divergent at the horizon, which is in contrast to the conventional calculations performed in the Kruskal coordinates. We resolve this conflict by invoking that the Kruskcal coordinates could be no longer proper coordinates at the horizon. In the Hartle-Hawking-Israel state, despite the negative finite proper energy density at the horizon, the Tolman temperature is diverg…
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 …
We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking's original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when q…
In 1989 Supplee described an apparent relativistic paradox on which a submarine seems to sink to observers at rest within the ocean, but it rather seems to float in the submarine proper frame. In this letter, we show that the paradox arises from a misuse of the Archimedes principle in the relativistic case. Considering first the special relativity, we show that any relativistic force field can be written in the Lorentz form, so that it can always be decomposed into a \emph{static} (electric-like) and a \emph{dynamic} (magnetic-like) part. These gravitomagnetic effects provide a relativistic fo…
The black hole information paradox presumes that quantum field theory in curved spacetime can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman's analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern i…
We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analog…
Quantum Geometry Effects in Quantum Field Theory: Hamiltonian constraint Generates Gravity-Matter Entanglement
School of Physics and Astronomy, Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University（北京师范大学物理与天文学院，教育部多尺度自旋物理重点实验室）
We present a table-top realization of a non-equilibrium quantum system described by a dynamical gauge field propagating on an effectively curved space and time manifold. The system is formed by neutral atoms interacting with both a conservative disordered optical field and a dissipative pumping field. In the presence of a sufficiently dark state, we demonstrate non-equilibrium behavior reminiscent of the information paradox in black hole physics. At a well-defined transition point, the analog of gauge-boson mass is seen to vanish, inducing scale-invariant behavior as a Higgs-like mechanism is …
Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge, Maxwell's equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell's equations need be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both can address the paradoxes. One is the Proca-type equation which contains a ph…
