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], ^{3}He-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 ^{3}He-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.

Living Rev. Relativity 14, (2011), 3
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