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Analogue Gravity

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Carlos Barcelo (IAA, Granada), Stefano Liberati (SISSA/ISAS, Trieste), Matt Visser (Victoria University of Wellington)

General Relativity and Quantum Cosmology · Submitted 13 May 2005 · 49 references

Pith's verdict: The field's standard review, updated through 2024: the physics is sound and the framing is mostly candid, but the copy-editing is rough and one universality slogan in §3.2.1 sits badly against §3.3.1.

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arXiv IDgr-qc/0505065 (version 4)
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CitationCarlos Barcelo (IAA, Granada), Matt Visser (Victoria University of Wellington), Stefano Liberati (SISSA/ISAS, Trieste). "Analogue Gravity." arXiv:gr-qc/0505065 (2005). https://pith.science/paper/IBWRNX4C
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The paper

The paper claims

Sound in a moving fluid obeys an effective Lorentzian metric, so tabletop horizons can probe Hawking-type physics; the review consolidates 43 years of models, history, and experiments.

The reading

Analogue gravity is the idea that some other physical system can reproduce the kinematics of a curved spacetime closely enough to be useful. The cleanest example is sound in a moving fluid. If you linearize the fluid equations around a background flow that is barotropic, inviscid, and irrotational, the small disturbances obey a wave equation that is exactly the d'Alembertian of a Lorentzian metric built algebraically from the local density, flow velocity, and speed of sound. That metric can have a horizon: a surface where the flow goes supersonic and sound can no longer swim upstream. The claim is that such a horizon should radiate phonons thermally, in direct analogy to Hawking radiation from a black hole, and that this happens for reasons that have nothing to do with Einstein's equations. The review walks through this derivation in detail, then surveys the many other systems where effective metrics appear: shallow water waves, dielectric media and the Gordon metric, Bose-Einstein condensates, superfluid helium, slow light, fibre optics, quantum fluids of light, graphene, and metamaterials. It also traces the history from Gordon in 1923 through Unruh's 1981 paper to the current experimental era, catalogues the models, and discusses what analogue experiments can and cannot tell us about quantum gravity, the information-loss problem, and the cosmological constant. The 2024 edition adds a substantial section on 2017-2024 work, including Steinhauer's BEC observations and optical and polariton experiments.
Extended reading notes

Core claim

Theorem 1 (Section 2.3): for a barotropic, inviscid, irrotational fluid, linearized sound obeys a d'Alembertian in an effective Lorentzian metric fixed algebraically by the background density, velocity, and sound speed. The review then asserts, following Unruh (1981), 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' (Section 3.2.1). If correct, horizons in fluids, BECs, and optical media should radiate thermally with a temperature set by the surface gravity of the effective metric.

Load-bearing premise

The review's framing that analogue experiments provide 'experimental validation of gravitational effects difficult to observe in their native form' rests on the premise that the analogy preserves enough structure for a laboratory measurement to count as evidence about the gravitational case. The authors themselves flag this as 'somewhat controversial' in footnote 3 of Section 1, pointing to Dardashti et al. (2017) and Evans and Thebault (2020). If the mapping from analogue to gravitational system does not support that inferential step, the programme's payoff shrinks to condensed-matter physics plus pedagogy, and the quantum-gravity motivation in Section 7 weakens accordingly.

Original abstract

Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights into related problems. Analogue models of gravity boast a long and distinguished history, dating back to the early years of general relativity. This review article delves into the history, aims, results, and future prospects of various analogue models. We begin by presenting a particularly simple example of an analogue model, then traverse the rich history and complex array of models discussed in the literature. The last decade has witnessed significant and sustained advances in analogue gravity, resulting in hundreds of published articles, workshops, and books. The future of the analogue gravity programme looks promising, with rapid technological advances on the experimental front and the potential for analogue models to inspire innovative approaches to the problem of quantum gravity on the theoretical front. Most of all, these recent years have seen the rise of an unprecedented collaboration and interplay between different communities that we believe will set a new standard for interdisciplinary research in the years to come.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,595 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.07 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights into related problems. Analogue models of gravity boast a long and distinguished history, dating back to the early years of general relativity. This review article delves into the history, aims, results, and future prospects of various analogue models. We begin by presenting a particularly simple example of an analogue model, then traverse the rich history and complex array of models discussed in the literature. The last decade has witnessed significant and sustained advances in analogue gravity, resulting in hundreds of published articles, workshops, and books. The future of the analogue gravity programme looks promising, with rapid technological advances on the experimental front and the potential for analogue models to inspire innovative approaches to the problem of quantum gravity on the theoretical front. Most of all, these recent years have seen the rise of an unprecedented collaboration and interplay between different communities that we believe will set a new standard for interdisciplinary research in the years to come.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Analogue gravity is a research programme that explores analogues of general relativistic gravitational fields within other physical systems, particularly but not exclusively in condensed matter systems, with the aim of gaining new insights into related problems. background 0.98 0.04 0.07 asserted 1.00
s1 Analogue models of gravity boast a long and distinguished history, dating back to the early years of general relativity. background 1.00 0.04 0.02 asserted 1.00
s2 This review article delves into the history, aims, results, and future prospects of various analogue models. contribution 0.97 0.27 0.04 asserted 0.96
s3 We begin by presenting a particularly simple example of an analogue model, then traverse the rich history and complex array of models discussed in the literature. contribution 0.61 0.38 0.02 asserted 0.83
s4 The last decade has witnessed significant and sustained advances in analogue gravity, resulting in hundreds of published articles, workshops, and books. background 0.97 0.06 0.06 asserted 1.00
s5 The future of the analogue gravity programme looks promising, with rapid technological advances on the experimental front and the potential for analogue models to inspire innovative approaches to the problem of quantum gravity on the theoretical front. future work 0.91 0.07 0.44 hedged possibility 0.54
s6 Most of all, these recent years have seen the rise of an unprecedented collaboration and interplay between different communities that we believe will set a new standard for interdisciplinary research in the years to come. interpretation 0.59 0.14 0.32 asserted 0.47

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Artistic impression of cascading sound cones (in the geometrical acoustics limit) form￾ing an acoustic black hole when supersonic flow tips the sound cones past the vertical. Analogies have played a very important role in physics and mathematics – they provide new ways of looking at problems that permit cross-fertilization of ideas among different branches of science. A carefully chosen analogy can be extremely useful in focusing attention on a specific problem, and in suggesting unexpected routes to a possible resolution. In this review article we shall focus on a specific analogy…
Figure 2. Artistic impression of trapped waves (in the physical acoustics limit) forming an acous￾tic black hole when supersonic flow forces the waves to move downstream. models what makes them really interesting — in that they can provide a coherent framework for (counter-factual) alternatives to standard general relativity and so allow us to test the robustness of some theoretical expectations w.r.t. to new physics.2 The most well-known of these analogies is based on the realization that sound waves in a moving fluid provide an analogue system for light waves in a curved spacetime. A…
Figure 3. A moving fluid will drag sound pulses along with it. Now the features of general relativity/gravity that one typically captures in an “analogue model” are the kinematic features that have to do with how fields (classical or quantum) are defined on curved spacetime, and the sine qua non 4 The need for a certain degree of caution regarding the allegedly straightforward physics of simple fluids might be inferred from the fact that the Clay Mathematics Institute is currently offering a US$ 1,000,000 Millennium Prize for significant progress on the question of existence and uniqueness of…
Figure 4. A moving fluid will tip the “sound cones” as it moves. Supersonic flow will tip the sound cones past the vertical. 2.3 Physical acoustics It is well known that for a static homogeneous inviscid fluid the propagation of sound waves is governed by the simple wave equation (Lamb 1932; Landau and Lifshitz 1959; Milne-Thomson 1968; Skudrzyk 1971) ∂ 2 t ϕ = c 2 s ∇ 2 ϕ. (5) Generalizing this result to a fluid that is non-homogeneous, or to a fluid that is in motion, possibly even in non-steady motion, is more subtle than it at first would appear. To derive a wave equation in this more
Figure 5. A moving fluid can form “trapped surfaces” when supersonic flow tips the sound cones past the vertical
Figure 6. A moving fluid can form an “acoustic horizon” when supersonic flow prevents upstream motion of sound waves. phonons rather than the more usual photons) cannot escape. This is actually the future event horizon. A past event horizon can be defined in terms of the boundary of the region that cannot be reached by incoming phonons – strictly speaking this requires us to define notions of past and future null infinities, but we will simply take all relevant incantations as understood. In particular, the event horizon is a null surface, the generators of which are null geodesics
Figure 7. A collapsing vortex geometry (draining bathtub): The green spirals denote streamlines of the fluid flow. The outer circle represents the ergo-surface (ergo-circle) while the inner circle represents the [outer] event horizon. Note that the sign of A is irrelevant in defining the ergo-surface and ergo-region: It does not matter if the vortex core is a source or a sink. The acoustic event horizon forms once the radial component of the fluid velocity exceeds the speed of sound, that is, at rhorizon = |A| cs . (99) The sign of A now makes a difference. For A < 0 we are dealing with a fut
Figure 8. Conformal diagram of an acoustic black hole
Figure 9. Conformal diagram of an acoustic black-hole–white-hole pair. Note the complete ab￾sence of singularities
Figure 10. Gravity waves in a shallow fluid basin with a background horizontal flow. realization of analogue horizons, it is a disadvantage in trying to detect analogue Hawking radiation as the relative temperature will necessarily be very low. (This is why, in order to have a possibility of experimentally observing (spontaneous) Hawking evaporation and other quantum phenomena, one would need to use ultra￾cold quantum fluids.) However, the gravity wave analogue can certainly serve to investigate the classical phenomena of mode mixing that underlies the quantum processes. It is this particular…
Figure 11. Domain wall configuration in 3He. A third way in which superfluid helium can be used to create analogues of gravitational configurations is the study of surface waves (or ripplons) on the interface between two different phases of 3He (Volovik 2002a,c). In particular, if we have a thin layer of 3He-A in contact with another thin layer of 3He-B, the oscillations of the contact surface “see” an effective metric of the form (Volovik 2002a,c) ds 2 = 1 (1 − αAαBU2) " −  1 − W2 − αAαBU 2  dt 2 − 2W·dx dt+dx ·dx# , (291)
Figure 12. Ripplons in the interface between two sliding superfluids. The advantage of using surface waves instead of bulk waves in superfluids is that one could create horizons without reaching supersonic speeds in the bulk fluid. This could alleviate the appearance of dynamical instabilities in the system, that in this case are controlled by the strength of the interaction of the ripplons with bulk degrees of freedom (Volovik 2002a,c). 4.2.3 Slow light in fluids The geometrical interpretation of the motion of light in dielectric media leads naturally to conjecture that the use of flowing…
Figure 13. The graphene hexagonal lattice is made of two inter-penetrating triangular lattices. Each is associated with one Fermi point. 2007b,a). If this proves to be experimentally correct, it will make graphene a good analogue model for a diverse set of spacetimes. This set, however, does not include black-hole spacetimes, as the curvatures mentioned above are purely spatial and do not affect the temporal components of the metric. 4.3 Going further As we said at the beginning of this section, this catalogue is by no means ex￾haustive, but we feel it covers key items in the history of the…
Figure 14. Velocity profile for a left going flow; the profile is dynamically modified with time so that it reaches the profile with a sonic point at some time in the asymptotic future. for the field and only some of them might exhibit Hawking radiation. This becomes more important when considering that the analogue models incor￾porate modified dispersion relations. An inappropriate preparation, together with modified dispersion relation effects, could completely eliminate Hawking radiation (Unruh and Sch¨utzhold 2005; Barcel´o et al. 2010b). 4. Another important issue is the need to…
Figure 15. The picture shows a subsonic dispersion relation as a relation ω − vk = ±cs|k|Γk for the three cases v = 0, v < cs and v > cs. In particular we plot a dispersion of the type Γk = (K/|k|) p tanh(k 2/K2) originally employed by Unruh. For subsonic velocities, v < cs, and ω less than a critical frequency ωc, the dispersion relation has four real roots, though for ω > ωc one only has two roots. For supersonic velocities v > cs, the dispersion relation has two real roots
Figure 16. The picture shows a supersonic dispersion relation as a relation ω − vk = ±cs|k|Γk, for the three cases v = 0, v < cs, and v > cs. In particular, we plot a dispersion of the type Γk = p 1 + k 2/K2. For subsonic velocities v < cs the dispersion relation has two real roots. For supersonic velocities v > cs, and ω less than a critical frequency ωc, the dispersion relation has four real roots, though for ω > ωc one again recovers two real roots. for these configurations, interpolates between its low energy, or geometric value, κ(ω = 0) = κ0 and a value of zero for ω → ωc. This…
Figure 17. One-dimensional velocity profile with a black-hole horizon. x v −c v(x)
Figure 18. One-dimensional velocity profile with a white-hole horizon. There are several classical instability analyses of these types of configurations in the literature (Garay et al. 2000, 2001; Leonhardt et al. 2002; Barcel´o et al. 2006a; Coutant and Parentani 2010; Finazzi and Parentani 2010). In these analyses one
Figure 19. One-dimensional velocity profile with a black-hole horizon and a white-hole horizon. v −c v(x) x x=−L/2 x=L/2 Periodically Identified
Figure 20. One-dimensional velocity profile in a ring; the fluid flow exhibits two sonic horizons, one of black hole type and the other of white-hole type. looks for the presence or absence of modes with a positive-imaginary-part eigenfre￾quency, under certain appropriate boundary conditions. The boundary condition in each asymptotic region can be described as outgoing, as in quasi-normal modes, or as convergent, meaning that at a particular instant of time the mode is expo￾nentially damped towards the asymptotic region. Let us mention that in Lorentz invariant theory these two types of…

Figures reproduced from arXiv:gr-qc/0505065 by the authors.

References
How later papers used it

314 later papers cite it

Evidence: substantial. 259 of the citing papers share no author with it, and 9 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 497 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Builds on it 1 paper · 1 by the same authors

By the same authors

  • Presented its construction as a generalization of the typical situation in analogue models of gravity, where Poincaré symmetries emerge from fundamental Galilean symmetries.

    Analogue Models for Emergent Gravity (2009) (same authors) · 0.81 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 5 papers with this label · 1 by the same authors

By the same authors

  • In order to describe the quantum fluctuations as massless scalar field propagating on top of an emergent acoustic metric, we use the Madelung representation for the condensate wavefunction [equation] and the quantum acoustic representation for the fluctuation [equation] where $n̂_1$ and $θ̂_1$ are two real scalar fields corresponding to phonon density and phase fluctuations, respectively [ref] .

    Gravitational Waves and Black Hole perturbations in Acoustic Analogues (2024) (same authors) · Theoretical setup · 0.93

Cites it as support 2 of 6 papers with this label · 1 by the same authors
  • The loss of thermodynamic description at $T_H ∼T_P/8π$ further suggests kinematic closure of evaporation [ref] .

    Dark Baryon Black Holes (2025) · Dark Baryon Black Holes Fate · 0.98

By the same authors

  • Inferred that UV–IR mixing is not invariably fatal from the fact that many condensed-matter analogue systems exhibit emergent Lorentz symmetry in the IR.

    Phenomenologically viable Lorentz-violating quantum gravity (2009) (same authors) · 0.98 · paraphrased: the licence does not allow quoting

How the literature uses it

268 arXiv papers cite this in 423 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 224 sentences without a confident label

Builds on it 1 paper
  • This construction can be seen as a generalization of the typical situation in analogue models of gravity [ref] where one has Poincaré symmetries emerging from fundamental Galilean symmetries [ref] .

    Analogue Models for Emergent Gravity · Emergence of time · 0.81

Uses its method or tool 5 papers
  • In order to describe the quantum fluctuations as massless scalar field propagating on top of an emergent acoustic metric, we use the Madelung representation for the condensate wavefunction [equation] and the quantum acoustic representation for the fluctuation [equation] where $n̂_1$ and $θ̂_1$ are two real scalar fields corresponding to phonon density and phase fluctuations, respectively [ref] .

    Gravitational Waves and Black Hole perturbations in Acoustic Analogues · Theoretical setup · 0.93

  • Now, to compute the Hawking temperature, we begin with the definition of the surface gravity for acoustic metrics [ref] [equation] Substituting the velocity profile $v(r) = b/r$ and evaluating at the horizon, where $v(r_H)^2= c_s^2$, we find that only the third term in the expansion contributes.

    Dynamical analog spacetimes from nonlinear perturbations in a topological material · Horizon location and Hawking Temperature of the analog System · 0.87

  • [equation] Expanding the Lagrangian around the classical solution chosen, we obtain: [equation] We can use a measure $=dx^d= d$ on $$ (where $$ depends on the metric $h_$, of course), and define an action for the fundamental field $ϕ$, which in turns implies an action for the perturbations [ref] .

    4d Deformed Special Relativity from Group Field Theories · GFT vs emergent analog gravity models · 0.90

Compares with it 2 papers
  • Compare this general relativistic acoustic metric with the non-relativistic limit, where the coordinates are most conveniently taken to be $x^a = (t; x^i)$ and where the d'Alembertian equation reduces to [ref] [equation] with $ρ_0≠ϱ_0$ now being the non-relativistic mass density, (not the relativistic energy density), and the meanings of $V_0$ and $h$ are suitably adjusted.

    Acoustic geometry for general relativistic barotropic irrotational fluid flow · The non-relativistic limit · 0.97

  • We point out that contrary to the situation in analog gravity models in condensed matter [ref] , our GFT models are non-geometric and far from usual geometrodynamics in their formalism, but at the same time are expected to encode quantum geometric information and to determine, in particular in their classical solutions, a (quantum and therefore classical) geometry for spacetime.

    The microscopic dynamics of quantum space as a group field theory · 4d case · 0.86

Cites it as support 6 papers
  • We emphasize the central importance of this result: It is a rigorous theorem of mathematical physics unambiguously demonstrating the existence of a curved spacetime whose geometry is defined by this acoustic metric — It is thus a proof of principle that spacetime metrics, and indeed Lorentzian geometries, can naturally “emerge” in situations where one would not a priori have expected them [ref] .

    Analogue spacetimes: Toy models for "quantum gravity'' · Introduction · 0.99

  • This immediately yields a clear hierarchy [equation] This separation of scales is essential for the robustness of Hawking-like radiation, as emphasized in Refs. [ref] .

    Smart Holes: Analogue black holes with the right temperature and entropy · Analogue black holes with the right temperature and entropy · 0.98

  • The loss of thermodynamic description at $T_H ∼T_P/8π$ further suggests kinematic closure of evaporation [ref] .

    Dark Baryon Black Holes · Dark Baryon Black Holes Fate · 0.98

Cites it as background 161 papers

Discussion

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