The key event in the “modern” period (though largely unrecognised at the time) was the 1981 publication
of Unruh’s paper “Experimental black hole evaporation” [607], which implemented an analogue model
based on fluid flow, and then used the power of that analogy to probe fundamental issues regarding
Hawking radiation from “real” general-relativistic black holes.
We believe that Unruh’s 1981 article represents the first observation of the now widely established fact that Hawking radiation has nothing to do with general relativity per se, but that Hawking radiation is instead a fundamental curved-space quantum field theory phenomenon that occurs whenever a horizon is present in an effective geometry.17 Though Unruh’s 1981 paper was seminal in this regard, it lay largely unnoticed for many years.
Some 10 years later Jacobson’s article “Black-hole evaporation and ultra-short distances” [307] used
Unruh’s analogy to build a physical model for the “trans-Planckian modes” believed to be relevant to
the Hawking radiation process. Progress then sped up with the relatively rapid appearance
of [308
] and [608
]. (This period also saw the independent rediscovery of the fluid analogue model
by one of the present authors [622], and the first explicit consideration of superfluids in this
regard [143].)
The later 1990s then saw continued work by Jacobson and his group [309, 310
, 148
, 146, 150
, 322
],
with new and rather different contributions coming in the form of the solid-state models considered by
Reznik [523
, 522
]. [285] is an attempt at connecting Hawking evaporation with the physics of collapsing
bubbles. This was part of a more general programme aimed at connecting black-hole thermodynamics with
perfect-fluid thermodynamics [286]. This period also saw the introduction of the more general class of superfluid
models considered by Volovik and his collaborators [644, 645, 359
, 183, 649, 647, 648, 326
, 651, 652],
more precise formulations of the notions of horizon, ergosphere, and surface gravity in analogue
models [624
, 626
], and discussions of the implications of analogue models regarding Bekenstein–Hawking
entropy [625, 626]. Optical models were considered in [389]. Finally, analogue spacetimes based on special
relativistic acoustics were considered in [72
].
By the year 2000, articles on one or another aspect of analogue gravity were appearing at the rate of over 20 per year, and it becomes impractical to summarise more than a selection of them.
Key developments in 2000 were the introduction, by Garay and collaborators, of the use of Bose–Einstein
condensates as a working fluid [231, 232
], and the extension of those ideas by the present authors [43].
Further afield, the trans-Planckian problem also reared its head in the context of cosmological
inflation, and analogue model ideas previously applied to Hawking radiation were reused in that
context [341, 457].
That year also marked the appearance of a review article on superfluid analogues [655], more work on
“near-horizon” physics [210], and the transference of the idea of analogue-inspired “multiple metric”
theories into cosmology, where they can be used as the basis for a precise definition of what is meant by a
VSL (“variable speed of light”) cosmology [58]. Models based on nonlinear electrodynamics were
investigated in [26], 3He-A based models were reconsidered in [316, 653], and “slow light”
models in quantum dielectrics were considered in [390
, 391, 382]. The most radical proposal to
appear in 2000 was that of Laughlin et al. [131
]. Based on taking a superfluid analogy rather
literally, they mooted an actual physical breakdown of general relativity at the horizon of a black
hole [131].
Additionally, the workshop on “Analogue models of general relativity”, held at CBPF (Rio de Janeiro)
gathered some 20 international participants and greatly stimulated the field, leading ultimately to the
publication of a book [470] in 2002.
This year saw more applications of analogue-inspired ideas to cosmological inflation [179, 441, 440
, 343
, 459
],
to neutron star cores [116], and to the cosmological constant [656, 658].
Closer to the heart of the analogue programme were the development of a “normal mode” analysis
in [44, 45, 637
], the development of dielectric analogues in [557], speculations regarding the possibly
emergent nature of Einstein gravity [50, 637
], and further developments regarding the use of 3He-A [178] as
an analogue for electromagnetism. Experimental proposals were considered in [48
, 637, 539
]. Vorticity was
discussed in [502], and the use of BECs as a model for the breakdown of Lorentz invariance in [636].
Analogue models based on nonlinear electrodynamics were discussed in [169]. Acoustics in an irrotational
vortex were investigated in [207].
The excitation spectrum in superfluids, specifically the fermion zero modes, were investigated in [654, 303], while the relationship between rotational friction in superfluids and super-radiance in rotating spacetimes was discussed in [104]. More work on “slow light” appeared in [91]. The possible role of Lorentz violations at ultra-high energy was emphasised in [312].
“What did we learn from studying acoustic black holes?” was the title and theme of Parentani’s article in
2002 [492], while Schützhold and Unruh developed a rather different fluid-based analogy based on gravity
waves in shallow water [560, 560
]. Super-radiance was investigated in [57
], while the propagation of
phonons and quasiparticles was discussed in [209, 208]. More work on “slow light” appeared in [211
, 509].
Applications to inflationary cosmology were developed in [460
], while analogue spacetimes relevant to
braneworld cosmologies were considered in [28].
The stability of an acoustic white hole was investigated in [386], while further developments regarding
analogue models based on nonlinear electrodynamics were presented by Novello and collaborators
in [170
, 171, 468
, 464
, 214
]. Though analogue models lead naturally to the idea of high-energy violations
of Lorentz invariance, it must be stressed that definite observational evidence for violations of Lorentz
invariance is lacking – in fact, there are rather strong constraints on how strong any possible Lorentz
violating effect might be [318
, 317
].
This year saw further discussion of analogue-inspired models for black-hole entropy and the cosmological
constant [661, 668], and the development of analogue models for FRW geometries [195, 194
, 46
, 177, 403
].
There were several further developments regarding the foundations of BEC-based models in [47
, 196
], while
analogue spacetimes in superfluid neutron stars were further investigated in [117].
Effective geometry was the theme in [466], while applications of nonlinear electrodynamics (and its
effective metric) to cosmology were presented in [467
]. Super-radiance was further investigated in [56
, 54],
while the limitations of the “slow light” analogue were explained in [612
]. Vachaspati argued for an analogy
between phase boundaries and acoustic horizons in [615]. Emergent relativity was again addressed in [378].
The review article by Burgess [98] emphasised the role of general relativity as an effective field theory – the
sine qua non for any attempt at interpreting general relativity as an emergent theory. The lecture notes by
Jacobson [313
] give a nice introduction to Hawking radiation and its connection to analogue
spacetimes.
The year 2004 saw the appearance of some 30 articles on (or closely related to) analogue models. Effective
geometries in astrophysics were discussed by Perez Bergliaffa [501], while the physical realizability of
acoustic Hawking radiation was addressed in [159, 616]. More cosmological issues were raised in [616, 675
],
while a specifically astrophysical use of the acoustic analogy was invoked in [160
, 161
, 162
].
BEC-based horizons were again considered in [249, 247], while backreaction effects were the focus of
attention in [25
, 23
, 344]. More issues relating to the simulation of FRW cosmologies were raised
in [204, 206
].
Unruh and Schützhold discussed the universality of the Hawking effect [613], and a new proposal for
possibly detecting Hawking radiation in an electromagnetic wave guide [562]. The causal structure
of analogue spacetimes was considered in [37
], while quasinormal modes attracted attention
in [69
, 392
, 112
, 452]. Two dimensional analogue models were considered in [101].
There were attempts at modeling the Kerr geometry [641], and generic “rotating” spacetimes [132], a
proposal for using analogue models to generate massive phonon modes in BECs [640, 642
], and an
extension of the usual formalism for representing weak-field gravitational lensing in terms of an analogue
refractive index [81]. Finally, we mention the development of yet more strong observational bounds on
possible ultra-high-energy Lorentz violation [319
, 320
].
The year 2005 saw continued and vigorous activity on the analogue model front. More studies of the
super-resonance phenomenon appeared [55, 193
, 347, 578], and a mini-survey was presented in [111].
Quasinormal modes again received attention in [135], while the Magnus force was reanalysed in terms of
the acoustic geometry in [699]. Singularities in the acoustic geometry are considered in [102], while
backreaction has received more attention in [559].
The original version of this Living Review appeared in May of 2005 [49], and since then activity has, if
anything, increased. Work on BEC-related models included [401, 402, 678, 642, 679, 605, 205], while
additional work on super-radiance [136], the background fluid flow [103], and quasinormal modes [537] also
appeared. Dynamical phase transitions were considered in [551], and astrophysical applications to accretion
flow in [2, 165]. The connection between white hole horizon and the classical notion of a “hydraulic jump”
was explored in [662] and in [572]. A “spacetime condensate” point of view was advocated in [299], and
analogue applications to “quantum teleportation” were considered in [243]. A nice survey of
analogue ideas and backreaction effects was presented in [21] (and related articles [23, 25
]).
Finally, we mention the appearance in 2005 of another Living Review, one that summarises and
systematises the very stringent bounds that have been developed on possible ultra-high-energy Lorentz
violation [435
].
A key article, which appeared in 2006, involved the “inverse” use of the acoustic metric to help understand hydrodynamic fluid flow in quark-gluon plasma [123]. The relationship between modified dispersion relations and Finsler spacetimes was discussed in [251]. Backreaction effects were again considered in [20].
Using analogue ideas as backdrop, Markopoulou developed a pre-geometric model for quantum gravity
in [421]. Analogue implications vis-a-vis entanglement entropy were discussed in [226, 225]. A microscopic
analysis of the micro-theory underlying acoustic Hawking radiation in a “piston” geometry appeared
in [248]. Volovik extended and explained his views on quantum hydrodynamics as a model for quantum
gravity in [664]. Applications to the cosmological constant were considered in [543]. More BEC-related
developments appeared in [680, 38, 39
, 29
, 24, 188, 189]. An analogue model based on a suspended
“shoestring” was explored in [282]. Super-resonance was again discussed in [352]. More analogue-inspired
work on black-hole accretion appeared in [164], while “ripplons” (quantised surface capillary waves) were
discussed in [663]. Modified dispersion relations again attracted attention [250], and analogue inspired
ideas concerning constrained systems were explored in [357]. Quasinormal frequencies were
considered in [134]. Finally, we emphasise particularly the realization that the occurrence of
Hawking-like radiation does not require the presence of an event horizon or even a trapped
region [38, 39].
Emergent geometry [16, 14, 15, 618] was an important theme in 2007, as were efforts at moving beyond
the semiclassical description [491]. BEC-based analogue models were adapted to investigating “signature
change events” in [684]. Acoustic cross-sections were considered in [156]. “Rimfall” was discussed
in [609].
Analogue-inspired ideas were adapted to the study of gravitational collapse in [40], while the importance
of nonlocal correlations in the Hawking flux was emphasized in [22
]. Quantum field theoretic anomalies
were considered in [345], while entanglement entropy was investigated in [324]. The specific shape of the de
Laval nozzle needed to acoustically reproduce linearised perturbations of the Schwarzschild geometry was
discussed in [1], and quasinormal frequencies were investigated in [692]. Superradiance and disclinations
were considered in [167]. Theoretical aspects of the circular hydraulic jump were investigated
in [519].
The use of analogue spacetimes as “toy models” for quantum gravity was emphasized in [643, 632].
Within the optics community Philbin, Leonhardt, and co-workers initiated the study of “fibre-optic black
holes” [505
, 504
]. Within the fluid dynamics community, wave-tank experiments were initiated [532
] by
Rousseaux and co-workers, who demonstrated the presence of negative phase-velocity waves.
Dissipation-induced breakdown of Lorentz invariance was considered by Parentani in [494, 495], and
BEC-based models continued to attract attention [676, 30
, 31, 333]. While analyzing quark matter,
acoustic metrics were found to be useful in [419] (see also [418]).
Analogues based on ion traps were considered by Schützhold in [558], while a toy model for
backreaction was explored in [414]. Further afield, analogue models were used to motivate a
“Abraham–Lorentz” interpretation of relativity in terms of a physically-real aether and physically-real
Lorentz–FitzGerald contraction [36]. In a similar vein analogue models were used to motivate a
counter-factual counter-historical approach to the Bohm versus Copenhagen interpretations of quantum
physics [463]. Analogue-inspired ideas regarding the possible “localization” of the origin of the Hawking
flux were investigated by Unruh in [610
]. Additionally, an analogue inspired analysis of accretion appeared
in [163], while astrophysical constraints on modified dispersion relations were improved and extended
in [409, 394].
This year saw the introduction of “quantum graphity” [358, 356], an analogue-inspired model for quantum
gravity. The BEC theme continued to generate attention [368], in particular regarding cosmological particle
production [677, 683
], and Hawking radiation [119
]. A mini-review appeared in [553]. The theme of
“emergence” was also represented in articles such as [255, 252
, 329]. Localization of the Hawking radiation
was again addressed in [563
], while sensitivity of the Hawking flux to the presence of superluminal
dispersion was considered in [33]. Astrophysical constraints on modified dispersion relations were again
considered in [408, 410], while applications to quark matter were investigated in [415, 417].
Possible applications to high-temperature superconductivity were reported in [444]. Quantum field
theoretic anomalies in an acoustic geometry were considered in [60, 691], while (2+1) acoustic
black-hole thermodynamics were investigated in [346]. Gravitational collapse was again discussed
in [40].
Gibbons and co-workers used analogue-based ideas in their analysis of general stationary
spacetimes, demonstrating that the spatial slices of stationary spacetimes are best thought of as a
special class of Finsler spaces, in particular, Randers spaces [246]. Attempts at developing
a generally useful notion of Finsler spacetime were discussed in [573, 574
], with Finslerian
applications to the Higgs mechanism being investigated in [569]. Signature change, now not in a
BEC context, was again addressed in [686
]. Black-hole lasers were considered in [388], and the
fluid-gravity correspondence in [5]. Backreaction of the Hawking flux was again considered in [556],
while the analogue physics of a “photon fluid” was considered in [420]. In [73] analogue ideas
were applied to polytrope models of Newtonian stars, while super-radiance was considered
in [598].
This year saw intriguing and unexpected relations develop between analogue spacetimes and Hořava
gravity [584, 585
, 634
, 666, 570]. These connections seem primarily related to the way Hořava’s
projectability condition interleaves with the ADM decomposition of the metric, and to the manner in which
Hořava’s distinguished spacetime foliation interleaves with the preferred use of Painlevé–Gullstrand-like
coordinates.
The theme of emergent gravity continues to play a role [300, 395, 571], as does the theme of nontrivial
dispersion relations [413
, 412
, 411, 396
, 437]. A variant of quantum graphity was further
developed in [268], and a matrix model implementation of analogue spacetime was developed
in [220]. Quasinormal modes were considered in [174, 700], with a survey appearing in [70].
Acoustic scattering was considered in [173]. Applications to quark matter were again investigated
in [416]. In [340], the universe was interpreted as a “soap film”. Nonlinear electrodynamics was
again considered in [260]. A model based on liquid crystals appeared in [500]. Attempts at
including backreaction in a cosmological fluid context were investigated in [451, 450]. Possible
experimental implementations of acoustic black holes using circulating ion rings are discussed
in [290
], while ultra-short laser pulses are considered in [187]. Signature change events were
again considered in [685
], while analogue-inspired lessons regarding the fundamental nature
of time were investigated in [330] and [254]. Non-canonical quantum fields were considered
in [304].
In [217, 218] analogue ideas are implemented in an unusual direction: fluid dynamics is used to model
aspects of quantum field theory. That the trans-Planckian and information loss problems are linked is
argued in [397]. The BEC paradigm for acoustic geometry is again discussed in [331] and [520],
while universal aspects of super-radiant scattering are considered in [524
]. Most remarkably, a
BEC-based black hole analogue was experimentally realised in [369
]. (See Sections 6.2 and
7.13.)
This current year has already (September) seen some 50 articles appear that can legitimately claim
to have either direct or tangential relationships to the analogue spacetime programme. Being
necessarily very selective, we first mention work related to “entropic” attempts at understanding the
“emergence” of general relativity and the spacetime “degrees of freedom” from the quantum
regime [483, 482, 130, 590, 355]. The use of correlations as a potential experimental probe has been
theoretically investigated in [19, 118
, 190
, 496
, 512
, 564
, 604], while an analysis of optimality
conditions for the detection of Hawking–Unruh radiation appeared in [13]. Entanglement issues
were explored in [427]. More work on “emergent horizons” has appeared in [552, 554, 555].
Relativistic fluids have been revisited in [639
], with specific applications to relativistic BECs being
reported in [191
]. Possible measurement protocols for Hawking radiation in ionic systems were
discussed in [291]. In [34] analogue spacetimes were used to carefully separate the notion of
“emergent manifold” from that of “emergent curvature”. Quantum graphity was again considered
in [110].
Step-function discontinuities in BECs were considered in [186, 438]. (Signature change can be viewed
as an extreme case of step-function discontinuity [684, 685, 686].) Black holes induced by
dielectric effects, and their associated Hawking radiation, were considered in [63]. The acoustic
geometry of polytrope rotating Newtonian stars was considered in [74]. Random fluids were
investigated in [365]. Finsler spacetime geometries were again considered in [575
], while the
relationship between analogue spacetimes and foundational mathematical relativity was discussed
in [139]. Further afield, analogue spacetimes were used as an aid to understanding “warp drive”
spacetimes [32].
Quantum sound in BECs was again investigated in [35], BEC-based particle creation in [367], and
BEC-based black hole lasers in [199
]. Optical effective geometries in Kerr media were discussed in [100].
2+1 dimensional draining-bathtub geometries were probed in [477]. Theoretical and historical analyses of
surface waves in a wave tank were presented in [531
]. Finally, we mention the stunning experimental
verification by Weinfurtner et al. of the existence of classical stimulated Hawking radiation in a wave
flume [682
], and the experimental detection of photons associated with a phase velocity horizon by
Belgiorno et al. [66
].
Interest in analogue models, analogue spacetimes, and analogue gravity is intense and shows no signs of abating. Interest in these ideas now extends far beyond the general relativity community, and there is significant promise for direct laboratory-based experimental input. We particularly wish to encourage the reader to keep an eye out for future developments regarding the possible experimental verification of the existence of Hawking radiation or the closely related Unruh radiation.
http://www.livingreviews.org/lrr-2011-3 |
Living Rev. Relativity 14, (2011), 3
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