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As a quantum analog of Cherenkov radiation, an inertial photon detector moving through a medium with constant refractive index $n$ may perceive the electromagnetic quantum fluctuations as real photons if its velocity $v$ exceeds the medium speed of light $c/n$. For dispersive Hopfield type media, we find this Ginzburg effect to extend to much lower $v$ because the phase velocity of light is very small near the medium resonance. In this regime, however, dissipation effects become important. Via an extended Hopfield model, we present a consistent treatment of quantum fluctuations in dispersive and dissipative media and derive the Ginzburg effect in such systems. Finally, we propose an experimental test., 11 pages, significantly extended version; with additional details on the pathway of dissipation (and comparisons to existing models) and on the scenario of fast atoms moving close to a medium

Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i.) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii.) While Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests, modified configurations, for example by relaunching the atoms, can mimic such tests tests under certain conditions. (iii.) Guided atom interferometers are comparable to atomic clocks. (iv.) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations., 21 pages, 3 figures

We comment on S. Carlip's recent Letter "Hiding the Cosmological Constant" [Phys. Rev. Lett. 123, 131302]., 1 page

A ground-state atom uniformly accelerated through the Minkowski vacuum can become excited by emitting an Unruh-Minkowski photon. We show that from the perspective of an accelerated atom, the sign of the frequency of the Unruh-Minkowski photons can be positive or negative depending on the acceleration direction. The accelerated atom becomes excited by emitting an Unruh-Minkowski photon which has negative frequency in the atom's frame, and decays by emitting a positive-frequency photon. This leads to interesting effects. For example, the photon emitted by accelerated ground-state atom cannot be absorbed by another ground-state atom accelerating in the same direction, but it can be absorbed by an excited atom or a ground-state atom accelerated in the opposite direction. We also show that similar effects take place for Cherenkov radiation. Namely, a Cherenkov photon emitted by an atom cannot be absorbed by another ground-state atom moving with the same velocity, but can be absorbed by an excited atom or a ground-state atom moving in the opposite direction.

There is widespread disagreement about how the general covariance of a theory affects its quantization. Without a complete quantum theory of gravity, one can examine quantum consequences of coordinate choices only in highly idealized `toy' models. In this work, we extend our previous analysis of a self-gravitating shell model [1], and demonstrate that coordinate freedom can be retained in a reduced phase space description of the system. We first consider a family of coordinate systems discussed by Martel and Poisson [2], which have time coordinates that coincide with the proper times of ingoing and outgoing geodesics (for concreteness, we only consider the former). Included in this family are Painlev\'e-Gullstrand coordinates, related to a network of infalling observers that are asymptotically at rest, and Eddington-Finkelstein coordinates, related to a network of infalling observers that travel at the speed of light. We then introduce "inflying" coordinates - a hybrid coordinate system that allows the infalling observers to be arbitrarily boosted from one member of the aforementioned family to another. We perform a phase space reduction using inflying coordinates with an unspecified boosting function, resulting in a reduced theory with residual coordinate freedom. Finally, we discuss quantization, and comment on the utility of the reduced system for the study of coordinate effects and the role of observers in quantum gravity., Comment: 12 pages, 2 figures

It is argued that it is best not to think of quantum mechanics as non-local, but rather that it is non-realistic. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum mechanics is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. Recently, some of the current authors proposed that the stochastic nature of the quantum vacuum can resolve this tension [Q, Wang, Z. Zhu, and W. G. Unruh, Phys. Rev. D 95, 103504, 2017]. By treating the fluctuations in the vacuum seriously and allowing fluctuations up to some high-energy cutoff at which Quantum Field Theory is believed to break down, a parametric resonance effect arises that leads to a slow expansion and acceleration. In this work, we thoroughly examine the implications of this proposal by investigating the resulting dynamics. First, we improve upon numerical calculations in the original work and show that convergence issues had overshadowed some important effects. Correct calculations reverse some of the conclusions in [Q. Wang, Z. Zhu, and W. G. Unruh, Phys. Rev. D 95, 103504, 2017], however the premise that parametric resonance can explain a very slowly accelerating expansion appears to remain sound. After improving the resolution and efficiency of the numerical tests, we explore a wider range of cutoff energies, and examine the effects of multiple particle fields. We introduce a simple model using the Mathieu equation (a prototypical example of parametric resonance), and find that it closely matches numerical results in regimes where its assumptions are valid. Using this model, we extrapolate to find that in a universe with 28 bosonic fields and a high-energy cutoff 40 times higher than the Planck energy, the acceleration would be comparable to what is observed., Comment: 19 pages, 12 figures

We present a simple model for stellar collapse and evaluate the quantum mechanical stress-energy tensor to argue that quantum effects do not play an important role for the collapse of astrophysical objects.

We study scattering of a composite quasiparticle, which possesses a degree of freedom corresponding to relative separation between two bound excitations, by a delta-like impurity potential on a one-dimensional discrete lattice. Firstly, we show that, due to specific properties of their dispersion, lattice excitations bind to impurities with both negative and positive potentials. We demonstrate that the finite size of the composite excitation leads to formation of multiple excitation-impurity bound states. The number and the degree of localization of these bound states depend on the signs and relative magnitudes of the impurity potential and the binding strength of two quasiparticles. We also report the existence of excitation-impurity bound states whose energies are located in the continuum band. Secondly, we study a change in the entanglement between the centre of mass and relative coordinate degrees of freedom of a biexciton wave packet during single impurity scattering and decoherence caused by it. For a composite quasiparticle on a lattice, the entanglement between its relative and centre of mass coordinate degrees of freedom arises naturally due to inseparability of the two-particle Hamiltonian. One of the main focuses of our study is to investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics., 15 pages, 8 figures, accepted by PRB

The complete gravitational collapse of a body in general relativity will result in the formation of a black hole. Although the black hole is classically stable, quantum particle creation processes will result in the emission of Hawking radiation to infinity and corresponding mass loss of the black hole, eventually resulting in the complete evaporation of the black hole. Semiclassical arguments strongly suggest that, in the process of black hole formation and evaporation, a pure quantum state will evolve to a mixed state, i.e., there will be "information loss." There has been considerable controversy over this issue for more than 40 years. In this review, we present the arguments in favor of information loss, and analyze some of the counter-arguments and alternative possibilities., 17 pages, 3 figures; Key Issues Review for Reports on Progress in Physics

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semi-classical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreovall, the amount of energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. We conclude that for any gravitational collapsing process within Einstein gravity and semi-classical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox., Comment: 6 pages, 2 figures

We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner--Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum system is the expectation value of the displacement operator, parametrized by the position and momentum displacements, and expectation values are evaluated as classical integrals over these parameters. The displacement operator is found to offer a complete orthogonal basis for operators, and some of its other properties are investigated. Connection to the Wigner distribution and Weyl procedure are discussed and examples are given., 6 pages + conclusion, references, and appendices

The physicist who 35 years ago proposed the construction of “dumb holes” to search for the analog of Hawking radiation is impressed by the recent experiment that looked for entangled thermal radiation from a tabletop horizon.

The temperature of an oscillator coupled to the vacuum state of a heat bath via ohmic coupling is non-zero, as measured by the reduced density matrix of the oscillator. This paper shows that the actual temperature, as measured by a thermometer is still zero (or in the thermal state of the bath, the temperature of the bath). The decoherence temperature is due to "false-decoherence", with the heat bath state being dragged along with the oscillator., Comment: 6 pages

Motivated by recent experimental efforts, we study a black hole analog induced by the propagation of a strong laser pulse in a nonlinear dielectric medium. Based on the Hopfield model (one pair of Sellmeier coefficients), we perform an analytic and fully relativistic microscopic derivation of the analog of Hawking radiation in this setup. The Hawking temperature is determined by the analog of the surface gravity (as expected), but we also find a frequency-dependent gray-body factor (i.e., a nonthermal spectrum at infinity) due to the breaking of conformal invariance in this setup., 16 pages REVTeX, 10 (sub)figures

The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region where the state cannot be distinguished from the vacuum state by any series of local measurements, including the energy density. For example, ``information'' (the correlations with the thermal emissions) need not be associated with any energy transport. The idea that black holes emit huge amounts of energy in their last stages because of all the information which must be emitted under the assumption of black hole unitarity is found to not necessarily be the case.

We present a mirror model moving in the quantum vacuum of a massive scalar field and study its motion under infinitely fluctuating quantum vacuum stress. The model is similar to the one in \cite{PhysRevD.89.085009}, but this time there is no divergent effective mass to weaken the effect of divergent vacuum energy density. We show that this kind of weakening is not necessary. The vacuum friction and strong anti-correlation property of the quantum vacuum are enough to confine the mirror's position fluctuations., 6 pages, 1 figure

We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer [1]. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed "universal" decoherence mechanism attributed to gravitational time dilation [2]. We note that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in [2] vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect., 7 pages. Minor revisions, accepted for publication in Foundations of Physics

Motivated by realistic scattering processes of composite systems, we study the dynamics of a two-particle bound system which is scattered at a mirror. The physics of the scattering process will be discussed in the cases when only one particle interacts directly with the mirror and when both particles are scattered directly. It is shown that the coherence between the transmitted and the reflected wave-packet becomes reduced due to the scattering process. When both particles interact directly with the mirror, the system exhibits long-lived resonances. The results should be of interest for interference experiments with composite systems., Comment: 5 pages, 11 figures

The cause of the collapse of the Tacoma Narrows Bridge has been a topic of much debate and confusion over the years. Many mischaracterizations of the observed phenomena have limited the understanding of the collapse even though there has always been an abundance of evidence in favor of a negative damping model. Negative damping, or positive feedback, is responsible for large amplitude oscillations in many systems, from musical instruments to the Tacoma Narrows Bridge failure. We discuss some of the more well known examples of positive feedback, and then show how the interaction of the wind with the oscillating bridge, especially the development of large scale vortices above and below the deck of the bridge, led to such a positive feedback instability. We support our model by computational, experimental, and historical data.

It is argued that Hawking radiation has indeed been measured and shown to posses a thermal spectrum, as predicted. This contention is based on three separate legs. The first is that the essential physics of the Hawking process for black holes can be modelled in other physical systems. The second is the white hole horizons are the time inverse of black hole horizons, and thus the physics of both is the same. The third is that the quantum emission, which is the Hawking process, is completely determined by measurements of the classical parameters of a linear physical system. The experiment conducted in 2010 fulfills all of these requirements, and is thus a true measurement of Hawking radiation., 5 fig, 10p

If quantum gravity does not lead to a breakdown of predictability, then Almheiri, Marolf, Polchinski and Sully (AMPS) have argued that an observer falling into a black hole can perform an experiment which verifies a violation of entanglement monogamy - that late time Hawking radiation is maximally entangled with early time Hawking radiation and also with infalling radiation - something impossible in quantum field theory. However, as pointed out by Hayden and Harlow, this experiment is infeasible, as the time required to perform the experiment is almost certainly longer than the lifetime of the black hole. Here we propose an alternative firewall experiment which could actually be performed within the black hole's lifetime. The alternative experiment involves forming an entangled black hole in which the unscrambling of information is precomputed on a quantum memory prior to the creation of the black hole and without acting on the matter which forms the black hole or emerges from it. This would allow an observer near a black hole to signal faster than light. As another application of our precomputing strategy, we show how one can produce entangled black holes which acts like ``flat mirrors'', in the sense that information comes out almost instantly (as in the Hayden-Preskill scenario), but also emerge unscrambled, so that it can actually be observed instantly as well. Finally, we prove that a black hole in thermal equilibrium with its own radiation, is uncorrelated with this radiation.

To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting interference pattern that would indicate coherence is fundamentally limited due to general relativistic effects. To eliminate the occurence of gravitational waves, we work in spherical symmetry, and construct the "beam" of the interferometer out of WKB states for an infinitesimally thin shell of matter. For internal consistency, we encode information about the beam optics within the dynamics of the shell itself, by arranging an ideal fluid on the surface of the shell with an equation of state that enforces beam-splitting and reflections. We then determine sufficient conditions for (interferometric) coherence to be fully present even after general relativistic corrections are introduced, test whether or not they can be satisfied, and remark on the implications of the results., Comment: 16 pages, 6 figures. v2: Minor revisions. Accepted for publication in Phys. Rev. D

Within quantum mechanics, a complete set of commutting observables can be found which describe the attributes of a system at a given time. However, the correct way to describe attributes of a system in time is still an open question. We discuss the difficulties in extending the standard approach of quantum mechanics to describe attributes of a system in time. We find that measuring when an event occurred and measuring that it occurred, are complimentary in Bohr's sense. To exemplify the differences between measurements at a given time and in time, we will compare Rovelli's recent proposal (quant-ph/9802020), to determine “at what time does a measurement occurred” with another model of a continuous measurement in time. Rovelli's scheme answers the question “has the measurement already occurred at a certain time?”, but does not answer to the more difficult question: “when did the measurement occur?” We also discuss the use of the probability current to measure the time at which a particle arrives to a certain location.

Stapp [Am. J. Phys. 65, 300 (1997)] has recently argued from a version of the Hardy-type experiments that quantum mechanics must be nonlocal, independent of any additional assumptions such as realism or hidden variables. I argue either that his conclusions do not follow from his assumptions or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

This paper presents an analysis of the radiation seen by an observer in circular acceleration, for a magnetic spin. This is applied to an electron in a storage ring, and the subtilty of the interaction of the spin with the spatial motion of the electron is explicated. This interaction is shown to be time dependent (in the radiating frame), which explains the strange results found for the electron's residual polarisation in the literature. Finally, some brief comments about the radiation emitted by an accelerating detector are made where it is shown that the spectrum is correlated in that particles are emitted in pairs., Comment: 21pp 7fig

The actual value of the quantum vacuum energy density is generally regarded as irrelevant in non-gravitational physics. However, this paper gives a non-gravitational system where this value does have physical significance. The system is a mirror with an internal degree of freedom which interacts with a scalar field. We find that the force exerted on the mirror by the field vacuum undergoes wild fluctuations with a magnitude proportional to the value of the vacuum energy density, which is mathematically infinite. This infinite fluctuating force gives infinite instantaneous acceleration of the mirror. We show that this infinite fluctuating force and infinite instantaneous acceleration make sense because they will not result in infinite fluctuation of the mirror's position. On the contrary, the mirror's fluctuating motion will be confined in a small region due to two special properties of the quantum vacuum: (1) the vacuum friction which resists the mirror's motion and (2) the strong anti-correlation of vacuum fluctuations which constantly changes the direction of the mirror's infinite instantaneous acceleration and thus cancels the effect of infinities to make the fluctuation of the mirror's position finite., 18pages, 6 figures

There is an analogy between the propagation of fields on a curved spacetime and shallow water waves in an open channel flow. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include wave horizons. Long (shallow water) waves propagating upstream towards this region are blocked and converted into short (deep water) waves. This is the analogue of the stimulated Hawking emission by a white hole (the time inverse of a black hole). The measurements of amplitudes of the converted waves demonstrate that they appear in pairs and are classically correlated; the spectra of the conversion process is described by a Boltzmann-distribution; and the Boltzmann-distribution is determined by the determined by the change in flow across the white hole horizon.

We give an overview of some fundamental quantum vacuum effects in curved space times that may be studied in earth based laboratories. In particular we review the concept of cosmological particle creation related to a contraction or expansion of the Universe.

The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying bottom topography. Most importantly, the conserved norm for the surface waves is derived, important for quantisation of these waves and their use in analogue models for black holes.

It has been argued that any evolution law taking pure states to mixed states in quantum field theory necessarily gives rise to violations of either causality or energy-momentum conservation, in such a way as to have unacceptable consequences for ordinary laboratory physics. We show here that this is not the case by giving a simple class of examples of Markovian evolution laws where rapid evolution from pure states to mixed states occurs for a wide class of states with appropriate properties at the ``Planck scale", suitable locality and causality properties hold for all states, and the deviations from ordinary dynamics (and, in particular, violations of energy-momentum conservation) are unobservably small for all states which one could expect to produce in a laboratory. In addition, we argue (via consideration of other, non-Markovian models) that conservation of energy and momentum for all states is not fundamentally incompatible with causality in dynamical models in which pure states evolve to mixed states., Comment: 19pages, RevTeX3, We have added a number of references and clarified the role of the Markovian approximation in the loss of energy conservation

The naive calculation of black hole evaporation makes the thermal emission depend on the arbitrary high frequency behavior of the theory where the theory is certainly wrong. Using the sonic analogue to black holes, ``dumb holes,'' I show numerically that a change in the dispersion relation at high frequencies does not seem to alter the evaporation process, lending weight to the reality of the black hole evaporation process. I also suggest a reason for the insensitivity of the process to the high frequency regime.

That decoherence can take place in the presence of energy conservation seems to be a poorly known fact. That lack of knowledge has for example bedevilled the discussion of the "black hole information" problem. I present a simple model which illustrates such energy free decoherence., Comment: 4 pages-- To appear in Phil Trans Roy Soc in special issue on Decoherence, ed. A. Hagar

Using a simple version of the model for the quantum measurement of a two-level system, the contention of Aharonov, Anandan, and Vaidman [Phys. Rev. A 47, 4616 (1993)] that one must in certain circumstances give the wave function an ontological as well as an epistemological significance is examined. I decide that their argument that the wave function of a system can be measured on a single system fails to establish the key point and that what they demonstrate is the ontological significance of certain operators in the theory, with the wave function playing its usual epistemological role.

In a recent paper Belgiorno {\em et al} claimed to have observed the analog of the Hawking effect because of the detection of radiation in a frequency range in which what they called "phase horizons" existed. They created rapidly moving pulses of light in a silica glass whose Kerr effect altered the refractive index to create those horizons. Unfortunately, while the observations are very interesting, the cause of the radiation is not understood, and we feel it is not justified to call this a detection of the Hawking effect in an analog system., 1 page

There is a mathematical analogy between the propagation of fields in a general relativistic space-time and long (shallow water) surface waves on moving water. Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. Similar arguments predict the same effect near wave horizons in fluid flow. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process., Comment: 7 pages, 5 figures. This version corrects a processing error in the final graph 5b which multiplied the vertical axis by 2. The graph, and the data used from it, have been corrected. Some minor typos have also been corrected. This version also uses TeX rather than Word

Inspired by the condensed-matter analogues of black holes, we study the quantum correlations across the event horizon reflecting the entanglement between the outgoing particles of the Hawking radiation and their in-falling partners. For a perfectly covariant theory, the total correlation is conserved in time and piles up arbitrary close to the horizon in the past, where it merges into the singularity of the vacuum two-point function at the light cone. After modifying the dispersion relation (i.e., breaking Lorentz invariance) for large $k$, on the other hand, the light cone is smeared out and the entanglement is not conserved but actually created in a given rate per unit time., 5 pages RevTeX, 1 figure

The embeddability of a straight cosmic string in a Friedmann-Robertson-Walker (FRW) universe is examined. Although previous suggestions that an exact embedding for a string with longitudinal tension equal to energy density is impossible are substantiated, it is shown that the deviations of either the external metric from the exact FRW metric or of the internal structure of the string from the exact tension equals energy density are expected to be very small, of the order of the square of the ratio of the string diameter (or the evacuated shell around the string) to the Hubble radius. Thus the lack of an exact mathematical embedding leads to negligible physical consequences. The problem with solving for an exact embedding of a string in the manner of the Swiss-cheese model is examined in detail, and it is shown that the metric in the evacuated region around the string is unique. That metric is determined to lowest order in the ratio of the evacuated region over the Hubble radius. The implications of this uniqueness for the Swiss-cheese embedding of a string are discussed.

We analyse the necessary and sufficient conditions for the occurrence of superradiance. Starting with a wave equation we examine the possibility of superradiance in terms of an effective potential and boundary conditions. In particular, we show that the existence of an ergoregion is not sufficient; an appropriate boundary condition, e.g. only ingoing group velocity waves at an event horizon, is also crucial. After applying our scheme to the standard examples of superradiance, we show that analogue models of gravity without an event horizon do not necessarily exhibit superradiance. Particularly, we show that the superradiant phenomenon is absent in purely rotating inviscid fluids with vorticity. We argue that there should be a catalogue of superradiant systems that can be found by focusing on the necessary and sufficient conditions outlined below., Comment: 4 pages; new version: new title no other changes

We present a gauge invariant argument that a nonlocal measure of second-order metric and matter perturbations dominate that of linear fluctuations in its effect on the gravitational field in 'slow-rolling' spacetimes., Version accepted by PRL (however, with correct non PRL format for arxiv posting). Clarified and expanded

We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $\omega(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $d\omega/dk$ and phase $\omega/k$ velocities evaluated at the frequency $\omega$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe'') and hence should not be a realistic model for the microscopic structure of quantum gravity.

The use of sonic analogues to black and white holes, called dumb or deaf holes, to understand the particle production by black holes is reviewed. The results suggest that the black hole particle production is a low-frequency and low-wavenumber process.