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3.1 Modern period

3.1.1 The years 1981-1999

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” [376Jump To The Next Citation Point], 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 relativity 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.15 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 ultrashort distances” [185Jump To The Next Citation Point] 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 [186Jump To The Next Citation Point] and [377Jump To The Next Citation Point378Jump To The Next Citation Point]. (This period also saw the independent rediscovery of the fluid analogue model by one of the present authors [387], and the first explicit consideration of superfluids in this regard [84].)

The later 1990’s then saw continued work by Jacobson and his group [187188Jump To The Next Citation Point88Jump To The Next Citation Point90Jump To The Next Citation Point198], with new and rather different contributions coming in the form of the solid state models considered by Reznik [319Jump To The Next Citation Point318Jump To The Next Citation Point].16 This period also saw the introduction of the more general class of superfluid models considered by Volovik and his collaborators [402403213Jump To The Next Citation Point110407405406199Jump To The Next Citation Point409410], more precise formulations of the notions of horizon, ergosphere, and surface gravity in analogue models [389Jump To The Next Citation Point391Jump To The Next Citation Point], and discussions of the implications of analogue models regarding Bekenstein-Hawking entropy [390391]. Finally, analogue spacetimes based on special relativistic acoustics were considered in [33]. 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.

3.1.2 The year 2000

Key developments in 2000 were the introduction, by Garay and collaborators, of the use of Bose-Einstein condensates as a working fluid [136Jump To The Next Citation Point137Jump To The Next Citation Point], and the extension of those ideas by the present authors [14]. 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 [205273].

That year also marked the appearance of a review article on superfluid analogues [413], more work on “near-horizon” physics [123], 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 [28Jump To The Next Citation Point]. Models based on nonlinear electrodynamics were investigated in [11], 3He - A based models were reconsidered in [193411], and “slow light” models in quantum dielectrics were considered in [235Jump To The Next Citation Point236231].

The most radical proposal to appear in 2000 was that of Laughlin et al. [76Jump To The Next Citation Point]. Based on taking a superfluid analogy rather literally they mooted an actual physical breakdown of general relativity at the horizon of a black hole [76].

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 the book [284Jump To The Next Citation Point] in 2002.

3.1.3 The year 2001

This year saw more applications of analogue-inspired ideas to cosmological inflation [107Jump To The Next Citation Point263262Jump To The Next Citation Point207Jump To The Next Citation Point275Jump To The Next Citation Point], to neutron star cores [66], and to the cosmological constant [414416].

Closer to the heart of the analogue programme were the development of a “normal mode” analysis in [1516Jump To The Next Citation Point398Jump To The Next Citation Point], the development of dielectric analogues in [342], speculations regarding the possibly emergent nature of Einstein gravity [20398Jump To The Next Citation Point], and further developments regarding the use of 3 He - A [106] as an analogue for electromagnetism. Experimental proposals were considered in [19Jump To The Next Citation Point398331].

Vorticity was discussed in [307], and the use of BECs as a model for the breakdown of Lorentz invariance in [397]. Analogue models based on nonlinear electrodynamics were discussed in [101]. Acoustics in an irrotational vortex were investigated in [120].

The excitation spectrum in superfluids, specifically the fermion zero modes, were investigated in [412182], while the relationship between rotational friction in superfluids and super-radiance in rotating spacetimes was discussed in [57]. More work on “slow light” appeared in [48]. The possible role of Lorentz violations at ultra-high energy was emphasised in [190].

3.1.4 The year 2002

“What did we learn from studying acoustic black holes?” was the title and theme of Parentani’s article in 2002 [300], while Schützhold and Unruh developed a rather different fluid-based analogy based on gravity waves in shallow water [344345Jump To The Next Citation Point]. Super-radiance was investigated in [27Jump To The Next Citation Point], while the propagation of phonons and quasiparticles was discussed in [122121]. More work on “slow light” appeared in [124Jump To The Next Citation Point311].

The stability of an acoustic white hole was investigated in [234], while further developments regarding analogue models based on nonlinear electrodynamics were presented by Novello and collaborators in [102Jump To The Next Citation Point103282Jump To The Next Citation Point278Jump To The Next Citation Point126Jump To The Next Citation Point]. Analogue spacetimes relevant to braneworld cosmologies were considered in [12].

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 [195Jump To The Next Citation Point194Jump To The Next Citation Point].

3.1.5 The year 2003

That year saw further discussion of analogue-inspired models for black hole entropy and the cosmological constant [419421], and the development of analogue models for FRW geometries [115Jump To The Next Citation Point114Jump To The Next Citation Point17Jump To The Next Citation Point105242Jump To The Next Citation Point]. There were several further developments regarding the foundations of BEC-based models in [18Jump To The Next Citation Point116Jump To The Next Citation Point], while analogue spacetimes in superfluid neutron stars were further investigated in [67].

Effective geometry was the theme in [280Jump To The Next Citation Point], while applications of nonlinear electrodynamics (and its effective metric) to cosmology were presented in [281Jump To The Next Citation Point]. Super-radiance was further investigated in [26Jump To The Next Citation Point24], while the limitations of the “slow light” analogue were explained in [379Jump To The Next Citation Point]. Vachaspati argued for an analogy between phase boundaries and acoustic horizons in [381]. Emergent relativity was again addressed in [227].

The review article by Burgess [53], 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 [191] give a nice introduction to Hawking radiation and its connection to analogue spacetimes.

3.1.6 The year 2004

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 [306], while the physical realizability of acoustic Hawking radiation was addressed in [95382Jump To The Next Citation Point]. More cosmological issues were raised in [382424Jump To The Next Citation Point], while a specifically astrophysical use of the acoustic analogy was invoked in [969798].

BEC-based horizons were again considered in [149148], while backreaction effects were the focus of attention in [10Jump To The Next Citation Point9Jump To The Next Citation Point208]. More issues relating to the simulation of FRW cosmologies were raised in [118119Jump To The Next Citation Point].

Unruh and Schützhold discussed the universality of the Hawking effect [380Jump To The Next Citation Point], and a new proposal for possibly detecting Hawking radiation in a electromagnetic wave guide [347]. The causal structure of analogue spacetimes was considered in [13Jump To The Next Citation Point], while quasinormal modes attracted attention in [31Jump To The Next Citation Point237Jump To The Next Citation Point64Jump To The Next Citation Point269]. Two dimensional analogue models were considered in [55].

There were attempts at modelling the Kerr geometry [401Jump To The Next Citation Point], and generic “rotating” spacetimes [77], a proposal for using analogue models to generate massive phonon modes in BECs [400], and an extension of the usual formalism for representing weak-field gravitational lensing in terms of an analogue refractive index [38].

Finally we mention the development of yet more strong observational bounds on possible ultra high energy Lorentz violation [196Jump To The Next Citation Point197Jump To The Next Citation Point].

3.1.7 The year 2005

The first few months of 2005 have seen continued and vigourous activity on the analogue model front.

More studies of the super-resonance phenomenon have appeared [25Jump To The Next Citation Point113Jump To The Next Citation Point209354], and a mini-survey was presented in [63]. Quasinormal modes have again received attention in  [78], while the Magnus force is reanalysed in terms of the acoustic geometry in [432]. Singularities in the acoustic geometry are considered in [56], while back-reaction has received more attention in [343].

Interest in analogue models is intense and shows no signs of abating.

We shall in the next subsection focus more precisely on the early history of analogue models, and specifically those that seem to us to have had a direct historical connection with the sustained burst of work carried out in the last 15 years.

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