International Centre for Theoretical Physics

u» IC/91/248

INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

HAWKING-LIKE EFFECTS: TOWARDS EXPERIMENTS

H. ROSU

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INTERNATIONAL ATOMIC ENERGY AGENCY

UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION MIRAMARE-TRIESTE

1CV91/248

International Atomic Energy Agency Motto " /ii the article E... I have collected and all tin facts I know United Nations Educational Scientific and Cultural Organization abovt the relative motion of the Ether " INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS J. Clerk Maxwell

1. Introduction The most famous scientific formula seems to be E = me2 which was settled by HAWKING-UKE EFFECTS: TOWARDS EXPERIMENTS * Einstein. However of the same rank is Hawking's formula

H. Rosu " T = (1) International Centre for Theoretical Physics, Trieste, Italy. including three fundamental physical constants.{ir is considered here as a pure ge- ometric constant). T is thermodynamic temperature and a is the acceleration parameter in the physical system under investigation. Hawking[l] got Kq.(l) in 1974 3 ABSTRACT for Schwarzschild black holes , being followed by Davies[,1] in 1975 and Unruh[4] in 1976 who obtained the same result for Rindler space-time/ uniform accelerat- We discuss the proposals made to detect Hawking radiation and Unruh radiation, and ing worldlines. The acceleration parameter is the so-called surface gravity in the former case and the proper acceleration of a quantum system (most often the elec- make brief comments on each of (hem. tron) in Hie latter case. The radiated spectrum in these two cases is exactly of black body type, almost forcing one to accept a truly thermal/thermodynamic interpretation as very natural one, although other viewpoints may be favoured {e.g., coherent effects[5j[6][7)[8| (9], or even better squeezing effects of a quantum field varuum[78][79]; Casimir-like effect9[52];ambiguity in defining positive and negative motlcs[10];instanton effects[llj). There exist standard methods to get these fun- MIRAMARE-TRIESTE damental thermal-like effects (e.g., Euclidean Green's functions[12][13], Bogolubov August 1991 mixing cc*fTicients[l4], instanton techniques[ll], analytic mappings)15]). Various aspects of those effects have been revealed in the vast literature that lias accumu- lated over the years ( we refer the reader to the well-known review papers ([16j[17] [18][19][20][21]). However we have to point out that we still lack a dedicated book although these effects are discussed with various degree of detail in black hole and QFT in curved apace-time books. Probably we should wait lirsl for a dedicated conference/symposium.

JJ'or a concise look al BH pliynics before Hawking elTwt «x\l\. Purl of a talk given at the Second Iniernational Wigner Symposium, Goslar, Germany, July 1991. Permanent address: Institute of Atomic Physics, P.O. Box Mg-6, Magurele Uucharest, Romania- 7690(1. The scope of the present short review paper is to present in chronological order the experimental settings that were proposed so far to detect such thermal- 2. Hawking Effect in Astrophysics liko effects, attaching very short comments to each of them. In cgs system Eq. (1) Hawking radiation is insignificant for stellar mass black holes and only primor- turns into: dial black holes(PBHs), i.e., those having a mass smaller than 1015j(this is the mass T = 4 x KT23 a (2) of a common Earth mountain) could have a detactable Hawking luminosity. The and therefore we need accelerations greater than IOM<7® (<7e is the mean Earth sur- point is that as early as 1976 Hawking and Page[24] concluded that mountain-mass face gravity) in order to have a "heat-bath" quantum vacuum at the level of only one black holes (they would have to be hadron-sized objects) formed in some way in the Kelvin. We are facing extremely small thermal-like quantum noises requiring ex- very early Universe (phase transitions,bubble colli«ions,string collapses, Zeldovitch- tremely strong non-adiabatic perturbations to be applied. Generally Hawking effect Harisson density perturbations) are at the present epoch in their final evaporation is considered to show up in the realm of astrophysics whereas Unruh-Davies effect is stages(Hawking explosions). The temperature of the PBHs passessiis the critical more appropriate to an extremely non-perturbative and non-linear electrodynamic mountain-mass h around 14 MeV, and they have been emitting on a time scale regime [22]. Indeed, the radiated Unruh power is 4.1 x 10~llV as compared with comparable with the lifetime of the Universe at the peak black body photon radia- the Larmor power which is 5.7 x 10~sla3 in the cgs units and one could see that the tion located at 14 MeV. The most simple experiment is consequently to measure the two radiations are comparable for a = 3 x lO30^®. Such accelerations are produced photon flux in the tens of MeV range by means of satellite-borne detectors. This by electric and/or magnetic fields that are one order of magnitude beyond the criti- has been done already in 1977-1978 but the measured 7 flux was seen to fall with cal field »nV/eft at which the spontaneous electron-positron pair production starts energy js £~3S without any evidence for a photon excess in the vicinity of 14 MeV. The negative result Was turned into a well-known limit on the number of PBHs on. The conclusion is that Unruh effect will be compeeted by other non-linear elec- per logarithmic mass interval at the critical mass, so-called Hawking-Page bound, trodynamic effects (first of all nonlinear Thomson scattering[22]). At the same time which however is strongly dependent on the cosmological parameters and the astro- Nikishov and Ritus(23] provided arguments against the Unruh heat-bath concept. physical premises(e.g., that PBHs have clustered also in galaxies).More intuitively To relate Hawking-like effects to Everyday Physics/Earth Laboratories we shall the Hawking-Page limit says that there cannot be more than 20 explosions per pc3 use throughout the paper the most simple vocabulary at our disposal. per year assuming galactic clustering of the critical PBHs. Recently Halzen and Zas[25] have reanalyzed the MeV limit on the number of critical PBHs by taking int* account the particle degrees of freedom of the standard model of quarks and leptons. They got an increase of one order of magnitude in their density and of two orders of magnitude in their explosion rate. New possibilities for detecting Hawking bursts in the TeV and PeV range open up by exploiting the capabilities of the new generation of air shower arrays and Cherenkov telescopes. For further details we refer the reader to the literature ([26][27][28] (29] [3O][31]|32][:13]).

3. Hydro dynamical Hawking Effect In a Physical Review Letter of 1981 Unruh[34] showed that a thermal spectrum of sound waves should be given out from the sonic horizon/Mach shock wave in ensemble of electrons in a uniform magnetic field at

Unruli did, in order to get, after quantising the sonic comoving field, a thermal flux tivistic electrons (0=1), Eq.(4) gives Pv = tanhir = 0.996, beyond the limiting

of phonons at a temperature polarization of Sokolov and Ternov[41J, Plim = ~^~ = 0.924. On the other hand^the function Pu(G) is very similar to the function PDK(G) obtained through QED calculations by Derbenev and Kondratenko[42]. The differ- 2k (3) ence is merely a shift of the latter along the positive G-axis with about 1.2 units. As Since usually the transonic transition is accompanied by turbulent instabilities shown by Bell and Leinaas when the Thomas precession of the electron is included in one would expect the sonic thermal- like spectrum at the shock to be much under the spin Hamiltonian a shift of 2 units is obtained for Pv{G). This suggests a more any experimental detection. Indeed to have a Planck spectrum peaked at only 1 K careful treatment of spin effects arising when one is going from the lab system to the gradient of the velocity at the shock has to reach lQOm/a per A. the circulating coordinate frame. A new spin Hamiltonian is introduced by Dell and Leinaas with a more complicated structure of the field vector in the scalar product Very recently Jacobson[35] has discussed the fluid flow analogy in the context of with the Pauli matrices. This ocnplicated structure takes into account the classical the question "would a black hole radiate if there were a. Planck scale cutoff in the rest external fields, the quantum radiation field and the fluctuations around the classical frame of the hole?". Trying to give an answer Jacobson developed a most interesting path. Within this more complete treatment, Bell and Leinaas are able to get to lin- superfluid black hole vacuum which certainly has to be further elaborated. ear order in the quantum fluctuations a Thomas like term and a third resonant term 4. Unruh Effect in Storage Rings directly related to the vertical fluctuations in the electron orbit which ate responsible The late J.S. Dell ("the cjuantiim engineer") and his collaborators J.M. Leiuaas for the spin transitions. The resonance factor f(G) induces an interesting variation and R.J. Hughes have imagined another experimental scheme connected to the Un- of the polarization close to the resonance. As 7 passes through it from below, the ruh effect. In the period 1983-1087 they have published a number of papers on the polarization falls from 92% to -17%, then increases again to 99% before stabilizing idea that the depolarising effects in electron storage rings could be interpreted in to 92% . This is the only clear difference from the standard QED. Such kind of res- terms of Unruh effect ([36],[37],[38], see also (39]). However the incomplete radiative onances have been considered before in the Russian literature but focusing strictly polarization of the electrons in storage rings has been first predicted in early sixties on their depolarizing effect. Their nature is related to the fact that the Fourier spec- in the framework of QED. Besides it is known that the circular vacuum noise does trum of the energy jumps associated with the quantum emission processes contains not, have the same universal thermal character as the linear Unruh noise. This is harmonics giving the usual resonance condition. As emphasized by Bell and Leinaas unfortunately an important drawback of the storage ring electron thermometry not a more direct experimental demonstration of the circular Unruh noise would be the to mention the very intricate spin physics. Keeping in mind these facts we shall measurement of the vertical fluctuations but this will be clearly a very difficult task make further comments, following the very clear discussion of Leinaas[40]. since such fluctuations are amongst the smallest orbit perturbations. At the same time tile measurement of the polarization variation closi; to tlic narrow resonance, 22 The circuliij- acceleration in the LEP machine is operator M has to be known for such fields. We refer the reader to the recent paper of Bayer and collaborators[45] There exist strong similarities between Hawking-like effects and Casimir elfcct. where one can find expressions for the real part of M (related to the anomalous mag- Indeed the global structure of the spacetime manifold is what really matters for netic moment of the electron) and the imaginary part (related to the probability of Hawking like effects. This is why the general features of Hawking's result could be emission). met already in the so-called moving mirror models.

Recently Ternov[46] has given a quantum generalization of the BMT evolution Hawking effect might be looked upon as a Casimir effect if we argue as follows. equation including the effects of Zilterbewegung and of the gradients of the magnetic The causal constraints generate peculiar surfaces (horizons) that may be considered field, again of much interest in the critical regime. as some kind of boundaries. Price(50] and Fabbri[51] have showirlong ago that the gravitational field of a black hole creates an effective potential barrier acting as a Very promising are at the same time the quasiclassical trajectory coherent good Conductor in the low frequency range and blocking the high frequency waves. states introduced by Hagrov and Maslov[47]. These states have been used in obtain- The barrier is very well localized near r = 1.5flj,. This barrier is the second plate ing another generalization of the BMT equation for spin in the case of an arbitrary in the Casimir setting. external torsion field[48] The analogy between Hawking effect and Casimir effect has been elaborated 5. Unruh Effect and Geonium Physics by Nugayev{52], who recently,based on itj predicted two regimes of black hole evapo- The very successful Geonium physics could help detecting the circular thermal- ration, ati anomalous skin-effect regime at low temperatures and a normal skin-effrct like vacuum noise. The proposal belongs to J. Rogers [49] being in our view one at higher temperatures[53]. of the most attractive. The idea of Rogers is to place a small superconducting Unfortunately the analogy is not complete. As was first shown by Ford[54], Penning trap in a microwave cavity. A single electron is constrained to move in a although the vacuum energy density in bounded space may have thermal represen- cyclotron orbit around the trap axis by a uniform magnetic field (Rogers figure is tations (see also |55]), the spectrum of the Casimir effect is not at all thermal. This 21 B = 150 kC!s). The circular proper acceleration is a = 6 x \0 g$ corresponding to could be seen when one is revealing the contribution of each frequency interval to T = 2.4 K. The velocity of the electron is maintained fixed (/? = 0.6) by means of the Casimir energy. 7. Unruh Effect and Nonadiabatic Casimir Effect 8. TJuruh Effect and Channeling

An experimental equivalent of a fast moving mirror could be a plasma front cre- The YERPHY group[57] has proposed to measure the Unruh radiation emit- ated when a gas is suddenly photoionized. This is the proposal of Yablonovileli[56]. ted in the Compton scattering of the channeled particles with the Planck spectrum The argument is thai the phase shift of the zero-point electromagnetic field trans- of the nonincrtial crystal vacuum. The proposal is based on the fact that the crys- mitted through a plasma window whose index of refrection is falling with time (from tallographic fields are acting with large transverse accelerations on the channeled 1 to 0) is the same as when reflected from an accelerating mirror. The argument, particles. is indeed correct as we could see by considering the hyperbolic motion. Since the The estimated transverse proper acceleration for positrons channeled in the velocity is I6 2 s (110) plane of a diamond crystal is a = 10 7 cm/s and at a 7 = 10 one could v = ctanh(—) 33 2 30 c (5) reach l0 cm/s = lO ^. where r is the observer's proper time, the Doppler shift frequency will be Working first in the particle instantaneous rest frame the Erevan group derived the spectral-angular distribution of the Unruh photons in that frame. Uy lx)rentss transforming to the lab system they got the number of Unruh photons per unit = u*oexp(-ar/c) (6) length of crystal and averaged over the channeling diameter. At about 7 = 10s the Unruh intensity becomes comparable with the bremsstrahlung. and consequently a plane wave of frequency wo turns into a wave with a time - Incidentally there is a parallel with some expcrimenls([r>8], [59],[60|) performed dependent frequency. Such waves are called chirped waves in nonlinear optics. in the last two years at LEP where the scattering of the LEP beam from the thermal The technique of producing plasma fronts in a gas by laser breakdown is well photon background in the beam pipe has been measured (the black body photons settled and blue shifts of about 10% have been observed in the transmitted laser emitted by the waits of the pipe have a mean energy of 0.07 eV). Fortunately the photon energy. effect is too small to affect the lifetime of the stored beams. hi his paper Yablonovitch works out a very simple model of a linear chirping In another work of the armenian group[61] the same type of calculations have due to a refractive index linearly decreasing with time. To have accelerations a = been applied to estimating the Unruh radiation generated by TeV electrons in a m 10' g9 the laser pulses should be less than 1 picosecond. Even more promising could uniform magnetic field as well as in a laser field. The Unruh radiation becomes 9 7 be the nonadiabatic photoionization of a semiconductor crystal in which case the predominant over the synchrotron radiation only when 7 = 10 for // = b-l0 Gs and refractive index can be reduced from 3.5 to 0 on the timescale of the optical pulse. consequently it is impossible to detect it even at the next generation of accelerators. As discussed by Yablonovitch the pump laser has to be tuned just below the Urbach Such a Unruh radiation could be appreciable in pulsar magnetospheres. tail of a direct-gap semiconductor in order to create weakly bound virtual electron- A circularly polarized laser field seems more promising since in this case the hole pairs which since are readily polarized contribute a large reactive component to Unruh radiation could be detactable at lower magnetic fields available at the energies the photocurrent. The background is due to the bremsstrahlungenussionproduced of the SSC (7 = 107). by real electron-hole pairs and to diminish it we need a crystal with a big Urbach 9. Hawkmg-like Effects and Free Electron Lasers (FELs) slope (the Urbach tail is a linear exponential behavior of the absorption coefficient). In principle Free Electron Lasers could be used to put into evidence Unruh We filially remark that the experimental interpretation is highlyamblRuous as radiation as well as Hawking r&diation[62],[63|. we could consider the phenomenon to be a single-cycle microwave squeezing and/or an inverse quadratic electro-optic effect with zero-point photons as input waves, and We first recall that in General Relativity it is welt known the so-called com- more theoretically as Unruh effect and nonadiabatic Casimir effect. plfxification trick (64] leading to new solutions of Binstein equations from a given

10 solution. In particular Peres[65] has shown long ago that by complexification oF the be better understood before addressing to more exotic aspects. As an example, Schwarzschild black hole one could get a gravitational tachyon. According to Peres Sessler[70] in his 1989 CAS lecture " Prospects for the FEL " speaks about an such procedures have been discussed by Rosen already in 1954. By this technique a untowerd number of new effects and discusses auperradiatire, plasma self-focusing, closed horizon is changed into an open (cone-like) horizon. The Mach cone and the chirping, and quantum mechanical behavior for the electrons and for the photons. Cherenkov shock wave are common examples of open horizons. On testing the photon-photon sector of quantum electrodynamics (i.e., non- On the other hand the electromagnetic emission makes always an important linear effects) with bright short-wavelength FEL with a high repetition rate have contribution to the radiation of a black hole horizon. With this in mind we have commented Becker and collaborators[71]. to add to the complexification trick another trick, that one in which gravitation is Finally strophotron FELs which are based on the channeling principle should supposed to be equivalent to an optical medium[66] . This is an old but not very be of interest for the Unruh radiation[72]. used method (Einstein was aware of it, and Tamm wrote papers as early as 1924). It is as if in this case gravitation looses its fundamental character turning into the 10. Unruh Effect and Anomalous Doppler Effect (ADE) constitutive equations of a dielectric medium with a variable refractive index. For When studied with the detector method Unruh effect is very close to anoma- example the propagation of electromagnetic Waves in the de Sitter space-time is lous Doppler effect (ADE) since in both cases the quantum detector is radiating equivalent to the same propagation in a Maxwell fisheye lens. This is a spherical "photons" while passing on the upper level and not on the lower one. The ADE-like lens with an index of refraction of the form: concept has been put forth by Unruh and Wald [73] without referring to it explicitly when they have considered the Unruh effect for a uniformly accelerated quantum n(p), 1+QV detector looked upon from the inertial reference frame. For the observer placed in the noninertial frame the photon is unobservable (it for p < R. The constant a gives the optical gradient and at the present time the belongs to the left wedge in the Rindler case) and a kind of postulate of inertia is GRIN technology is at the level of a = 0.1 - 0.2 mm'1. acting on the detector in the sense of an unrestless uniform accelerated motion. In our previous works we have proposed to study the electromagnetic radiation When the observer places himself in an inertial reference frame then he is able of the black hole horizon on the equivalent scheme of a Cherenkov-Walsh FEL[67], to observe both the excited quantum detector ( furnishing at the same time energy In such a FEL a relativistic electron beam of very good quality passes over a thin to it) and the "photons". By writing down the energy-momentum conservation law dielectric guide or through a channel in it, interacting with the axial component he will be inclined to say that the "photons" are emitted precisely when the detector of the TM modes of the guiding structure. The stimulated emission occurs in the is excited. modes with a phase velocity slightly less than the velocity of the beam. Neglecting recoil and absorption the elementary radiation events for a two-level There exists a chance for Hawking-like effects to be seen in this experimental detector with the change of the detector proper energy denoted by St are classified configuration iff the lining structure is chosen to be a GRIN material with a very according to the photon energy formula [74]: high optical gradient (one may think of quartz and fused silica which are common materials in GRIN optics). Of course the 7 of the beam will be also very high. In 6t this setting Hawking-like noise will be related to the waveguide dispersion of the (8) liner. Also gas-loaded FELs considered by Pantell's group should be taken into account [68]. where 7 is the relativistic velocity factor (7 > 1) and I) is the Doppler directivity Unfortunately there are many sources of noise in FEL devices (the most com- factor mon is the shot noise[69]), and moreover a lot of other phenomena are waiting to D- I~(vnfc)cos9 (9)

12 11 T\\c discussion of signs in Eq.(8) implies 3 cases as follows: the paradox is solved in a very convenient way. Another well-known result in the squeezing theory is that the photon number statistics of a squeezed vacuum state is D> 0 for normal Doppler effect (NDE, 6e < 0) always super-Poisson. I) = 0 for Chcrenkov effect (CE, St = 0, undetermined case) The conclusion of this section is that some real photons show up in one of the D< 0 for anomalous Doppler effect (ADE, St > 0) Consequently for a quantum quadratures of the squeezed zero point fluctuations of a noniuertial vacuum. As system endowed with internal degrees of freedom the stationary population of levels was shown by Grishchuk and Sidoiov[79] the in and out states in the Schwarzschikl is determined by the probability of radiation in the ADE and NDE regions. The black hole case are related by a two-mode squeeze operator with the same squeezing possibility of doing population inversion by means of ADE has been tackled in the parameter for all modes given by: literature {see section 8 in [63] and references therein).

Moreover we can modify the index of refraction in the Doppler factor in such tanhar = exp(-87rGA/u) (11) a manner as to get the ADE conditions already at sublight velocities. In this way a more direct link to the Unruh effect is available as has been shown also by Brevik On gravitationally squeezed light has commented J.T. Wheeler{80] . and Kolbenstvedt[75]. 12. Conclusions and Perspectives We mention here that one way to look at negative energy waves in plasma We have updated our previous works on the proposals made so far to detect physics is to consider them as a manifestation of induced ADE elementary events(see thermal-like vacuum noise. This research field is extremely rich covering a large the book of Nezlin[76]). Very recently Pfirsch[77j delivered a series of lectures on the range of physical situations, and I have tried to touch upon all its aspects as they nonlinear instabilities in plasmas related to the existence of linear negative energy reveal themselves to me at the present time. Of course there is always something perturbations, expressed in terms of specific creation and annihilation operators, more to say and/or something which has not been said in the proper manner. and also presented a discussion of the complete solution of the three-oscillator case with Cherry-like nonlinear coupling. We would like to mention here one of the first applications of Hawking-like effects namely to explain the thermal spectrum in the transverse energy of the pro- 11. Hawking-like Effects and Squeezing duced particles observed in high-energy collisions. Salam and Strathdee[81] have IJow could be that in the inertial vacuum we have only zero point fluctuations considered Hawking effect of Kerr-Newman black solitonic solutions in strong grav- but when we change the coordinates to a noninertial reference frame the new vacuum ity J,o be responsible for the ET thermal spectrum. Hosoya[82j(see also [83]) ap- stales which could be appropriately defined are thermal-like states containing real plied moving mirror effects to the thermal gluon production and very recently the photons. Where do the real photons come from? YERPHY group[84) estimated the contribution of Unruh effect to the soft photon production by quarks as entailed into the observed anomalous low pr photons in In our opinion[78], the most natural answer to such a paradox is given in the K+p interections at P = 70GeV/c. squeezing physics. Every noninertial vacuum , no matter the way it is defined is a squeezed vacuum with respect to the inertial one. The squeezing parameter is The idea of relating the hadronic temperature to the Unruh effect is rather related to the boost transformation from inertial to noninertial coordinates. The old [85], One should note the recently introduced hadronic temperature in terms of point is that squeezed vacuum states have a nonzero mean photon number Lorentz-squeezed hadrons [86], Other vivid pictures have to do with the relationship between the limiting < n >— sinha r (10) Hagedorn temperature/maximal acceleration and ttie Hawking temperature(87J, the where r is the squeezing parameter characterizing the boost transformation. Con- space-time duality symmetry and the role played by strings in the last stages of sequently any iioninertiaJ/gravilatiotial vacuum is no longer a truly vacuum and black hole evaporation[88]. All these topics and many others are without any doubt

13 in the pure theoretical framework devoided of any practical feature for many years References to come if not for ever. Another topic to be considered in the future is the connection between Berry's [1] S.W. Hawking, "Black Hole Explosions?" Nature 248 ,30-31 (1974) phase and the noninertial/gravitational thermal-like effects,[89],[90],[91]. Indeed, [2] R. Ruffini, J.A. Wheeler, "Introducing the BH" Physics Today 24, 30-41 (Jan- Berry phase could be related to the so-called Wigner angle and also to the Thomas uary 1971) precession which in turn could be considered as a squeezing phenomenon [90][92]. [3] P.C.W. Davies, "Scalar Particle Production in Schwarzschild and Itindler met- Suppose now that one day we will be almost sure that a certain object or group rics" J. Phys.AS, 609-616 (1975) of objects are black holes. Of course, we shall have from them the power spectrum and we would like to determine the horizon area- temperature distribution. Taking [4] W.G. Unruh, "Notes on BH evaporation" Phys. Rev.D14 870-892 (1976) a black body spectrum as granted we will face the inverse black body problem for a quantum (horizon) surface[93]. This problem is not at all trivial even for classical [5] K. Freese, C.T, Hill, M. Mueller, "Covariant Functional Schrodinger Formalism surfaces. and Application to the Hawking Effect", Nucl.Phys. B255, 693-716 (1985)

Also C.R. Stephens has written interesting works on the similarities between [6] C.T. Hill, "One Loop Operator Matrix Elements in the Unruh Vacuum", black holes and penetration through a harmonic oscillator barrier[94], as well as on Nucl.Phys. B277, 547-574 (1986) the Hawking effect for gauge field configurations[95]. [7] T.q;. Lee, "BH Radiation", PTP Suppl.85, 271-278 (1985) Last but not least the clear-cut aspects of Unruh effect in the realm of nonlinear quantum electrodynamica! cffects[22] should be further studied taking into account [81 T.D. Lee, "Are BHs Black Bodies?", Nucl.Phys, B264, 437-486 (1986) the quasi-reality of some proposed experimental schemes. [9] L.N. Pringle, "Rindler Observers, Correlated States, Boundary Conditions , Acknowledgements and the Meaning of the Thermal Spectrum" Phys.Rev. D39, 2178-2186 (1989)

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