Rafael D. Sorkin
I introduce the concept of *entanglement entropy* (as it's now called) and point out that it follows an *area law* which renders it a suitable source of black hole entropy. I also suggest to conceive the latter as residing on the horizon at approximately one bit per "Planckian plaquette".
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Duality of Ryu-Takayanagi surfaces inside and outside the horizon
该研究通过重构视界内RT表面面积，展示了黑洞内部时空可通过视界外的自由度实现互补性。
Islands Far Outside the Horizon
本研究针对半经典引力中纠缠孤岛信息重构的有效场论失效问题，计算四维Schwarzschild黑洞大角动量Hawking模式的孤岛，发现其突出视界外距离大于普朗克尺度，为实验验证黑洞信息佯谬的两种解决方案提供可能。
The spontaneous excitation of a two-level atom held static outside a four dimensional Schwarzschild black hole and in interaction with a massless scalar field in the Boulware, Unruh and Hartle-Hawking vacuum is investigated and the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy are calculated separately. We find that for the Boulware vacuum, the spontaneous excitation does not occur and the ground state atoms are stable, while the spontaneous emission rate for excited atoms in the Boulware vacuum, which is well-behaved at the eve…
Based on the idea that the vacuum fluctuations of electromagnetic fields can induce instantaneous correlated dipoles, we study the far-zone Casimir-Polder potential between two atoms in the Boulware, Unruh and Hartle-Hawking vacua outside a Schwarzschild black hole. We show that, at spatial infinity, the Casimir-Polder potential in the Boulware vacuum is similar to that in the Minkowski vacuum in flat spacetime with a behavior of $R^{-7}$, so is in the Unruh vacuum as a result of the backscattering of the Hawking radiation from the black hole off the spacetime curvature. However, the interatom…
We examine the Hawking effect by studying the asymptotic entanglement of two mutually independent two-level atoms placed at a fixed radial distance outside a Schwarzschild black hole in the framework of open quantum systems. We treat the two-atom system as an open quantum system in a bath of fluctuating quantized massless scalar fields in vacuum and calculate the concurrence, a measurement of entanglement, of the equilibrium state of the system at large times, for the Unruh, Hartle-Hawking and Boulware vacua respectively. We find, for all three vacuum cases, that the atoms turn out to be entan…
We investigate a quasi-local energy naturally introduced by Kodama's prescription for a spherically symmetric space-time with a positive cosmological constant $Λ$. We find that this quasi-local energy is well behaved inside a cosmological horizon. However, when there is a scalar field with a long enough Compton wavelength, the quasi-local energy diverges in the course of its time evolution outside the cosmological horizon. This means that the quasi-local energy has a meaning only inside the cosmological horizon.
Quantum black holes: inside and outside
该研究通过Wheeler-DeWitt方程分析，指出黑洞视界外部需用相干态描述，内部则为多个相干态的叠加，从而将黑洞视为高度量子宏观物体，为理解信息丢失悖论提供新视角。
Making a connection between observations of cosmological correlation functions and those calculated from theories of the early universe requires that these quantities are conserved through the periods of the universe which we do not understand. In this paper, the results of [0810.2831] are extended to show that tree-approximation correlation functions of Heisenberg picture operators for the reduced spatial metric are constant outside the horizon during local thermal equilibrium with no non-zero conserved quantum numbers.
We study, by separately calculating the contributions of vacuum fluctuations and radiation reaction to the atomic energy level shift, the Lamb shift of a static two-level atom interacting with real massless scalar fields in the Boulware, Unruh and Hartle-Hawking vacuums outside a Schwarzschild black hole. We find that in the Boulware vacuum, the Lamb shift gets a correction arising as a result of the backscattering of vacuum field modes off the space-time curvature, which is reminiscent of the correction to the Lamb shift induced by the presence of cavities. However, when the Unruh and Hartle-…
We prove uniqueness of the near-horizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum near-horizon geometries.
We show that there is a classical metric satisfying the Einstein equations outside a finite spacetime region where matter collapses into a black hole and then emerges from a white hole. We compute this metric explicitly. We show how quantum theory determines the (long) time for the process to happen. A black hole can thus quantum-tunnel into a white hole. For this to happen, quantum gravity should affect the metric also in a small region outside the horizon: we show that contrary to what is commonly assumed, this is not forbidden by causality or by the semiclassical approximation, because quan…
We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of Schwarzschild observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a…
With the back-reaction of Hawking radiation taken into consideration, the work of Kawai, Matsuo and Yokokura has shown that, under a few assumptions, the collapse of matter does not lead to event horizon nor apparent horizon. In this paper, we relax their assumptions and elaborate on the space-time geometry of a generic collapsing body with spherical symmetry. The geometry outside the collapsing sphere is found to be approximated by the geometry outside the white-hole horizon, hence the collapsing matter remains outside the Schwarzschild radius. As particles in Hawking radiation are created in…
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in…
In this paper, we investigate the dynamics inside and outside of black-branes in anti de Sitter space by numerical simulations using double-null formalism. We prepare a charged planar matter shell which, due to a negative cosmological constant, collapses and dynamically forms a black-brane with an apparent horizon, a singularity and a Cauchy horizon. The gravitational collapse cannot form a naked overcharged black-brane and hence weak cosmic censorship is safe. Although mass inflation occurs, the effect is much milder than in the case of charged black holes; hence, strong cosmic censorship see…
The vacuum expectation value of the current density for a charged scalar field is investigated in Rindler spacetime with a part of spatial dimensions compactified to a torus. It is assumed that the field is prepared in the Fulling-Rindler vacuum state. For general values of the phases in the periodicity conditions and the lengths of compact dimensions, the expressions are provided for the Hadamard function and vacuum currents. The current density along compact dimensions is a periodic function of the magnetic flux enclosed by those dimensions and vanishes on the Rindler horizon. The obtained r…
We obtain an analytic expression for the vacuum polarization on the horizon of the Schwarzschild black hole threaded by an infinite cosmic string. This calculation relies on a generalized Heine identity for Legendre functions which we derive without using specific properties of the Legendre functions themselves.
If a system falls through a black hole horizon, then its information is lost to an observer at infinity. But we argue that the {\it accessible} information is lost {\it before} the horizon is crossed. The temperature of the hole limits information carrying signals from a system that has fallen too close to the horizon. Extremal holes have T=0, but there is a minimum energy required to emit a quantum in the short proper time left before the horizon is crossed. If we attempt to bring the system back to infinity for observation, then acceleration radiation destroys the information. All three cons…
It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial metric divided by the square of the Robertson--Walker scale factor $a$) is time-independent, though with an arbitrary dependence on co-moving coordinates, and all perturbations to the other metric components and to all matter variables vanish, to leading order in $1/a$. The corrections are of order $1/a^2$, and are explicitly given for the reduced metric in…
We consider radiative processes of a quantum system composed by two identical two-level atoms in a black-hole background. We assume that these identical two-level atoms are placed at fixed radial distances outside a Schwarzschild black hole and interacting with a quantum electromagnetic field prepared in one of the usual vacuum states, namely the Boulware, Unruh or the Hartle-Hawking vacuum states. We study the structure of the rate of variation of the atomic energy. The intention is to identify in a quantitative way the contributions of vacuum fluctuations and radiation reaction to the entang…
Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outsi…
We consider an Unruh-DeWitt detector interacting with a massless Dirac field. Assuming that the detector is moving along an hyperbolic trajectory, we modeled the effects of fluctuations in the event horizon using a Dirac equation with random coefficients. First, we develop the perturbation theory for the fermionic field in a random media. Further we evaluate corrections due to the randomness in the response function associated to different model detectors.
Modular theory of operator algebras and the associated KMS property are used to obtain a unified description for the thermal aspects of the standard heat bath situation and those caused by quantum vacuum fluctuations from localization. An algebraic variant of lightfront holography reveals that the vacuum polarization on wedge horizons is compressed into the lightray direction. Their absence in the transverse direction is the prerequisite to an area (generalized Bekenstein-) behavior of entropy-like measures which reveal the loss of purity of the vacuum due to restrictions to wedges and their h…
Several recently found properties of the event horizon of black holes are discussed. One of them is the reflection of the incoming particles on the horizon. A particle approaching the black hole can bounce on the horizon back, into the outside world, which drastically reduces the absorption cross section in the infrared region. Another, though related phenomenon takes place for particles inside the horizon. A locked inside particle has, in fact, an opportunity to escape into the outside world. Thus, the confinement inside the horizon is not absolute. The escape from within the interior region …
We show that static metrics solving vacuum Einstein equations (possibly with a cosmological constant) are one-sided analytic at non-degenerate Killing horizons. We further prove analyticity in a two-sided neighborhood of "bifurcate horizons". It is a pleasure to dedicate this work to Prof. Staruszkiewicz, on the occasion of his 65th birthday.
Trans-planckian frequencies can be mimicked outside a black-hole horizon as a tail of an exponentially large amplitude wave that is mostly hidden behind the horizon. The present proposal requires implementing a final state condition. This condition involves only frequencies below the cutoff scale. It may be interpreted as a condition on the singularity. Despite the introduction of the cutoff, the Hawking radiation is restored for static observers. Freely falling observers see empty space outside the horizon, but are "heated" as they cross the horizon.
The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
该研究定义并计算了Schwarzschild黑洞视界正则化真空态的费米子纠缠熵，借助变量分离与Dirac传播子积分表示，得出其正比于视界上已占据角动量模式数的结论。
We show that the response rate of (i) a static source interacting with Hawking radiation of massless scalar field in Schwarzschild spacetime (with the Unruh vacuum) and that of (ii) a uniformly accelerated source with the same proper acceleration in Minkowski spacetime (with the Minkowski vacuum) are equal. We show that this equality will not hold if the Unruh vacuum is replaced by the Hartle-Hawking vacuum. It is verified that the source responds to the Hawking radiation near the horizon as if it were at rest in a thermal bath in Minkowski spacetime with the same temperature. It is also verif…
We calculate, in the framework of open quantum systems, the ground state energy-level shift for a static two-level atom outside a spherically symmetric black hole in interaction with fluctuating massless scalar fields in the Boulware and Unruh vacuums. We find that the energy-level shift is position-dependent and thus gives rise to a force on the atom besides the classical gravitational force. For the case of the Boulware vacuum which represents a star that has not collapsed through its event horizon, this force is attractive near the horizon and is repulsive far away from the black hole with …
We present a simple proof of the non-existence of degenerate components of the event horizon in static, vacuum, regular, four-dimensional black hole spacetimes. We discuss the generalisation to higher dimensions and the inclusion of a cosmological constant.
We address the question whether or not two electrically charged elementary particles can Coulomb scatter if one of these particles is inside the Schwarzschild black-hole horizon and the other outside. It can be shown that the quantum process is consistent with the local energy-momentum conservation law. This result implies that across-horizon scattering is a physical effect, relevant to astrophysical black holes. We propose a Gedankenexperiment which uses the quantum scattering process to transfer information from inside the black-hole horizon to outside.
We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.
Vacuum polarization of massive scalar fields in a thermal state at arbitrary temperature is studied near the horizon of a Reissner-Nordström black hole. We derived an analytic form of $<ϕ^2>$ approximately in the large mass limit near the black hole horizon. We uses the zeroth order WKB approximation and power series expansion near the horizon for the Euclideanized mode function. Our formula for the vacuum polarization shows regular behavior on the horizon if the temperature of the scalar field is equal to the Hawking temperature of the black hole. The finite part of the vacuum polarization ag…
Using the FermiDirac distribution function, Balart and Vagenas gave a charged spherically symmetric regular black hole, which is a solution of Einstein field equations coupled to a nonlinear electrodynamics. In fact, the regular black hole is a Reissner-Nordstrom (RN) black hole when a metric function is given a Taylor expansion to first order approximations. It does not have a curvature singularity at the origin,but the RN black hole does. Both black hole metrics have horizons and similar asymptotic behaviors, and satisfy the weak energy conditions everywhere. They are almost the same in phot…
We compute the super-Hubble evolution of non-Gaussianity of primordial curvature perturbations in two-field inflation models by employing two formalisms: delta N and covariant formalisms. Although two formalisms treat the evolution of fluctuations radically different, we show that the formulas of f_{NL} parameter agree quantitatively with each other within 1 % accuracy. We analytically find that the amplitude of f_{NL} decays no faster than a^{-3} as the inflationary trajectory reaches to the adiabatic limit for generic potentials.
A cosmological event horizon develops in a vacuum-dominated Friedmann universe. The Schwarschild radius of the vacuum energy within the horizon equals the horizon radius. Black hole thermodynamics and the holographic conjecture indicate a finite number of degrees of freedom within the horizon. The average energy per degree of freedom equals the energy of a massless quantum with wavelength of the horizon circumference. This suggests identifying the degrees of freedom with the presence or absence, in each Planck area on one horizon quadrant, of a 0S2 vibrational mode of the horizon with the z ax…
The aim of this article is to study the effect of an Event Horizon on the entanglement of the Quantum Vacuum and how entanglement, together with the Holographic Principle, may explain the current value of the Cosmological Constant, in light of recent theories. Entanglement is tested for vacuum states very near and very far from the Horizon of a de Sitter Universe, using the Peres-Horodecki (PPT) criterion. A scalar vacuum field ($\hatϕ$) is averaged inside two boxes of volume $V$ in different spatial positions such that it acquires the structure of a bipartite Quantum Harmonic Oscillator, for …
Vacuum Polarization and Persistence on the Black Hole Horizon
本文基于 Schwinger 变分原理求得 Schwarzschild 黑洞的精确单圈有效作用量，揭示真空极化极点与留数分别对应 Hawking 辐射主导项和总通量。
In Class. Quantum Grav. 35 (2018) 155015 we have introduced the notion of "Multiple Killing Horizon" and analyzed some of its general properties. Multiple Killing Horizons are Killing horizons for two or more linearly independent Killing vectors simultaneously. In this paper we focus on the vacuum case, possibly with cosmological constant, and study the emergence of Multiple Killing Horizons in terms of characteristic initial value problems for two transversally intersecting null hypersurfaces. As a relevant outcome, a more general definition of Near Horizon Geometry is put forward. This new d…
We consider extremal black hole solutions to the vacuum Einstein equations in dimensions greater than five. We prove that the near-horizon geometry of any such black hole must possess an SO(2,1) symmetry in a special case where one has an enhanced rotational symmetry group. We construct examples of vacuum near-horizon geometries using the extremal Myers-Perry black holes and boosted Myers-Perry strings. The latter lead to near-horizon geometries of black ring topology, which in odd spacetime dimensions have the correct number rotational symmetries to describe an asymptotically flat black objec…
Vacuum asymptotically flat Robinson-Trautman spacetimes are a well known class of spacetimes exhibiting outgoing gravitational radiation. In this paper we describe a method of locating the past apparent horizon in these spacetimes, and discuss the properties of the horizon. We show that the past apparent horizon is non-timelike, and that its surface area is a decreasing function of the retarded time. A numerical simulation of the apparent horizon is also discussed.
We describe static, brane--like, solutions to vacuum Einstein's equations in D = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutions have positive ADM mass but no horizon. The curvature invariants are finite everywhere except at r = 0 where r is the radial coordinate in the m + 1 dimensional space. The presence of n \ge 1 extra dimensions is crucial for these properties. Such solutions may be naturally anticipated if Mathur's fuzzball proposal for black holes is correct.
We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy-momentum tensor in the near-horizon region.
We consider the near-horizon geometries of extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry in 4d, two commuting rotational symmetries in 5d and in both cases non-toroidal horizon topology. In 4d we determine the most general near-horizon geometry of such a black hole, and prove it is the same as the near-horizon limit of the extremal Kerr-AdS(4) black hole. In 5d, without a cosmological constant, we determine all possible near-horizon geometries …
We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.
Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII and IX, as they approach the big bang singularity. It is known since 2001 that generic Bianchi IX spacetimes converge towards the so-called Mixmaster attractor as time goes towards the singularity. We extend this result to the case of Bianchi VIII vacuum. The BKL picture suggests that particle horizons should form, i.e. spatially separate regions should cau…
We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.
We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T…
A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta…
We analyze the late-time decay of scalar perturbations in extremal Reissner-Nordstrom spacetime. We consider individual spherical-harmonic modes $l$ of a test massless scalar field, restricting our attention to initial data of compact support, with generic regular behavior across the horizon. We obtain a decay rate $\propto t^{-(2l+3)}$ (just like in Schwarzschild) for incident waves scattered by the black hole. However, for waves originating at the horizon's neighborhood we obtain a slightly slower decay, $\propto t^{-(2l+2)}$. We discuss relations to previous works.
I show that in the Boulware vacuum (1) all standard (point-wise and averaged) energy conditions are violated throughout the exterior region---all the way from spatial infinity down to the event horizon, and (2) outside the event horizon the standard point-wise energy conditions are violated in a maximal manner: they are violated at all points and for all null/timelike vectors. (The region inside the event horizon is considerably messier, and of dubious physical relevance. Nevertheless the standard point-wise energy conditions also seem to be violated even inside the event horizon.) This is rat…
We prove uniqueness theorems for asymptotically flat, stationary, extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-extremal case, these problems may be cast as boundary value problems on the two dimensional orbit space. We show that the orbit space for solutions with one extremal horizon is homeomorphic to an infinite strip, where the two boundaries correspond to the rotational axes, and the two asymptotic regions correspond to spatial infinity and the near-horizon geometry. In four dimensions th…
The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian excitations at the horizon can be supported by the infinite Tolman temperature at the horizon. In an exactly soluble model, we explicitly show that the firewall necessarily emerges out of the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is divergent in essence due to the infinitely blueshifted negative ingoing flux cr…
Quantum fluctuations in the background geometry of a black hole are shown to affect the propagation of matter states falling into the black hole in a foliation that corresponds to observations purely outside the horizon. A state that starts as a Minkowski vacuum at past null infinity gets entangled with the gravity sector, so that close to the horizon it can be represented by a statistical ensemble of orthogonal states. We construct an operator connecting the different states and comment on the possible physical meaning of the above construction. The induced energy-momentum tensor of these sta…
We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar's conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non expanding, shear free surface is characterized. The results…
The results of a recent paper [0808.2909] are generalized. A more detailed proof is presented that under essentially all conditions, the non-linear classical equations governing matter and gravitation in cosmology have ``adiabatic'' solutions in which, far outside the horizon, in a suitable gauge, the reduced spatial metric $g_{ij}({\bf x},t)/a^2(t)$ becomes a time-independent function ${\cal G}_{ij}({\bf x})$, and all perturbations to the other metric components and to all matter variables vanish. The corrections are of order $a^{-2}$, and their ${\bf x}$-dependence is now explicitly given in…
It has recently been shown that the Einstein equation can be derived by demanding a non-equilibrium entropy balance law dS = dQ/T + dS_i hold for all local acceleration horizons through each point in spacetime. The entropy change dS is proportional to the change in horizon area while dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. The internal entropy production term dS_i is proportional to the squared shear of the horizon and the ratio of the proportionality constant to the area entropy density is \hbar/4π. Here w…
Modes just outside the horizon of a typical old black hole are thermally entangled with distant Hawking radiation. This precludes their entangled purity with interior modes, leading to a firewall. Identifying the interior with the distant radiation ("A=R_B", "ER=EPR") can resolve the entanglement conflict. But the map must adjust for any interactions, or else the firewall will reappear if the Hawking radiation scatters off the CMB. With a self-correcting map, an infalling observer is unable to excite the vacuum near the horizon. This allows the horizon to be locally detected and so violates th…
Suppose we allow a system to fall freely from infinity to a point near (but not beyond) the horizon of a black hole. We note that in a sense the information in the system is already lost to an observer at infinity. Once the system is too close to the horizon it does not have enough energy to send its information back because the information carrying quanta would get redshifted to a point where they get confused with Hawking radiation. If one attempts to turn the infalling system around and bring it back to infinity for observation then it will experience Unruh radiation from the required accel…
Motivated by recent work suggesting observably large spacetime fluctuations in the causal development of an empty region of flat space, we conjecture that these metric fluctuations can be quantitatively described in terms of a conformal field theory of near-horizon vacuum states. One consequence of this conjecture is that fluctuations in the modular Hamiltonian $ΔK$ of a causal diamond are equal to the entanglement entropy: $\langle ΔK^2 \rangle = \langle K \rangle = \frac{A(Σ_{d-2})}{4 G_d}$, where $A(Σ_{d-2})$ is the area of the entangling surface in $d$ dimensions. Our conjecture applies to…
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