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Analogue Gravity Living Rev. Relativity, 14, (2011), 3 LIVINGREVIEWS http://www.livingreviews.org/lrr-2011-3 (Update of lrr-2005-12) in relativity Analogue Gravity Carlos Barcel´o Instituto de Astrof´ısicade Andaluc´ıa(IAA-CSIC) Glorieta de la Astronom´ıa, 18008 Granada, Spain email: [email protected] http://www.iaa.csic.es/ Stefano Liberati SISSA International School for Advanced Studies Via Bonomea 265, I-34136 Trieste, Italy, and INFN, Sezione di Trieste, Trieste, Italy email: [email protected] http://www.sissa.it/~liberati Matt Visser School of Mathematics, Statistics, and Operations Research Victoria University of Wellington; PO Box 600 Wellington 6140, New Zealand email: [email protected] http://www.msor.victoria.ac.nz/~visser Accepted on 28 February 2011 Published on 11 May 2011 Abstract Analogue gravity is a research programme which investigates analogues of general relativis- tic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Ana- logue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in par- ticular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity). This review is licensed under a Creative Commons Attribution-Non-Commercial-NoDerivs 3.0 Germany License. http://creativecommons.org/licenses/by-nc-nd/3.0/de/ Imprint / Terms of Use Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am M¨uhlenberg 1, 14476 Potsdam, Germany. ISSN 1433-8351. This review is licensed under a Creative Commons Attribution-Non-Commercial-NoDerivs 3.0 Germany License: http://creativecommons.org/licenses/by-nc-nd/3.0/de/ Because a Living Reviews article can evolve over time, we recommend to cite the article as follows: Carlos Barcel´o,Stefano Liberati and Matt Visser, \Analogue Gravity", Living Rev. Relativity, 14, (2011), 3. [Online Article]: cited [<date>], http://www.livingreviews.org/lrr-2011-3 The date given as <date> then uniquely identifies the version of the article you are referring to. Article Revisions Living Reviews supports two ways of keeping its articles up-to-date: Fast-track revision A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here. Major update A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number. For detailed documentation of an article's evolution, please refer to the history document of the article's online version at http://www.livingreviews.org/lrr-2011-3. 11 May 2011: Completely revised and updated previous version. Significantly extended Sec- tions 2.4, 3, 4.1, 4.2, 5, and 7. Introduced new Section 6. Eight new figures have been added. The number of references increased from 434 to 702. Contents 1 Introduction 7 1.1 Overview ......................................... 8 1.2 Motivations ........................................ 8 1.3 Going further ....................................... 9 2 The Simplest Example of an Analogue Spacetime 10 2.1 Background ........................................ 10 2.2 Geometrical acoustics .................................. 11 2.3 Physical acoustics ..................................... 12 2.4 General features of the acoustic metric ......................... 16 2.4.1 Horizons and ergo-regions ............................ 18 2.4.2 Surface gravity .................................. 20 2.4.3 Example: vortex geometry ............................ 25 2.4.4 Example: slab geometry ............................. 27 2.4.5 Example: Painlev´e{Gullstrandgeometry .................... 27 2.4.6 Causal structure ................................. 29 2.5 Cosmological metrics ................................... 30 2.5.1 Explosion ..................................... 30 2.5.2 Varying the effective speed of light ....................... 32 2.6 Regaining geometric acoustics .............................. 33 2.7 Generalizing the physical model ............................. 34 2.7.1 External forces .................................. 34 2.7.2 The role of dimension .............................. 35 2.7.3 Adding vorticity ................................. 36 2.8 Simple Lagrangian meta-model ............................. 36 2.9 Going further ....................................... 39 3 History 40 3.1 Historical period ..................................... 40 3.1.1 Optics { the Gordon metric ........................... 40 3.1.2 Acoustics ..................................... 41 3.1.3 Surface waves ................................... 42 3.2 Modern period ...................................... 42 3.2.1 The years 1981{1999 ............................... 42 3.2.2 The year 2000 .................................. 43 3.2.3 The year 2001 .................................. 43 3.2.4 The year 2002 .................................. 43 3.2.5 The year 2003 .................................. 44 3.2.6 The year 2004 .................................. 44 3.2.7 The year 2005 .................................. 44 3.2.8 The year 2006 .................................. 45 3.2.9 The year 2007 .................................. 45 3.2.10 The year 2008 .................................. 46 3.2.11 The year 2009 .................................. 46 3.2.12 The year 2010 .................................. 47 3.2.13 The future? .................................... 47 3.3 Going further ....................................... 47 4 A Catalogue of Models 50 4.1 Classical models ..................................... 50 4.1.1 Classical sound .................................. 50 4.1.2 Sound in relativistic hydrodynamics ...................... 50 4.1.3 Shallow water waves (gravity waves) ...................... 52 4.1.4 More general water waves ............................ 53 4.1.5 Classical refractive index ............................ 55 4.1.6 Normal mode meta-models ........................... 58 4.2 Quantum models ..................................... 63 4.2.1 Bose{Einstein condensates ............................ 63 4.2.2 The heliocentric universe ............................ 70 4.2.3 Slow light in fluids ................................ 72 4.2.4 Slow light in fibre optics ............................. 75 4.2.5 Lattice models .................................. 75 4.2.6 Graphene ..................................... 76 4.3 Going further ....................................... 77 5 Phenomenology of Analogue Models 78 5.1 Hawking radiation .................................... 78 5.1.1 Basics ....................................... 78 5.1.2 UV robustness .................................. 80 5.1.3 General conditions for Hawking radiation ................... 86 5.1.4 Source of the Hawking quanta ......................... 86 5.1.5 Which surface gravity? .............................. 86 5.1.6 How to detect Hawking radiation: Correlations . 87 5.1.7 Open issues .................................... 88 5.1.8 Solid state and lattice models .......................... 89 5.1.9 Analogue spacetimes as background gestalt . 89 5.2 Dynamical stability of horizons ............................. 90 5.2.1 Classical stability of the background (no MDR) . 90 5.2.2 Semiclassical stability of the background (no MDR) . 91 5.2.3 Classical stability of the background (MDR in BECs) . 91 5.2.4 Black holes, white holes, and rings ....................... 92 5.3 Super-radiance ...................................... 95 5.4 Cosmological particle production ............................ 96 5.5 Bose novae: an example of the reverse flow of information? . 96 5.6 Romulan cloaking devices ................................ 97 5.7 Going further ....................................... 98 6 Experimental efforts 99 6.1 Wave tank experiments ................................. 99 6.2 Bose{Einstein condensate experiments . 100 6.3 Differentially-rotating flows in superfluid helium . 100 6.4 Fibre-optic models .................................... 100 6.5 Going further ....................................... 101 7 Towards a Theory of Quantum Gravity? 102 7.1 Backreaction ....................................... 102 7.2 Equivalence principle ................................... 103 7.3 Nontrivial dispersion as Einstein-aether theory . 104 7.4 Diffeomorphism invariance ................................ 105 7.5 Effective spin-two particles ............................... 105 7.6 Weinberg{Witten theorem ...............................
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