Analogue Gravity Phenomenology Analogue Spacetimes and Horizons, from Theory to Experiment PDF
Preview Analogue Gravity Phenomenology Analogue Spacetimes and Horizons, from Theory to Experiment
Lecture Notes in Physics Volume 870 FoundingEditors W.Beiglböck J.Ehlers K.Hepp H.Weidenmüller EditorialBoard B.-G.Englert,Singapore,Singapore U.Frisch,Nice,France P.Hänggi,Augsburg,Germany W.Hillebrandt,Garching,Germany M.Hjort-Jensen,Oslo,Norway R.A.L.Jones,Sheffield,UK H.vonLöhneysen,Karlsruhe,Germany M.S.Longair,Cambridge,UK M.L.Mangano,Geneva,Switzerland J.-F.Pinton,Lyon,France J.-M.Raimond,Paris,France A.Rubio,Donostia,SanSebastian,Spain M.Salmhofer,Heidelberg,Germany D.Sornette,Zurich,Switzerland S.Theisen,Potsdam,Germany D.Vollhardt,Augsburg,Germany W.Weise,Garching,GermanyandTrento,Italy Forfurthervolumes: www.springer.com/series/5304 The Lecture Notes in Physics TheseriesLectureNotesinPhysics(LNP),foundedin1969,reportsnewdevelop- ments in physics research and teaching—quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging mate- rialbetweenadvancedgraduatetextbooksandtheforefrontofresearchandtoserve threepurposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialistresearchersfromrelatedareas • to be a source of advanced teaching material for specialized seminars, courses andschools Both monographs and multi-author volumes will be considered for publication. Editedvolumesshould,however,consistofaverylimitednumberofcontributions only.ProceedingswillnotbeconsideredforLNP. Volumes published in LNP are disseminated both in print and in electronic for- mats,theelectronicarchivebeingavailableatspringerlink.com.Theseriescontent isindexed,abstractedandreferencedbymanyabstractingandinformationservices, bibliographicnetworks,subscriptionagencies,librarynetworks,andconsortia. Proposals should be sent to a member of the Editorial Board, or directly to the managingeditoratSpringer: ChristianCaron SpringerHeidelberg PhysicsEditorialDepartmentI Tiergartenstrasse17 69121Heidelberg/Germany [email protected] Daniele Faccio (cid:2) Francesco Belgiorno (cid:2) Sergio Cacciatori (cid:2) Vittorio Gorini (cid:2) Stefano Liberati (cid:2) Ugo Moschella Editors Analogue Gravity Phenomenology Analogue Spacetimes and Horizons, from Theory to Experiment Editors DanieleFaccio VittorioGorini SchoolofEngineeringandPhysical DipartimentodiScienzaeAltaTecnologia Sciences,InstituteofPhotonicsand Universitàdell’Insubria QuantumSciences,ScottishUniversities Como,Italy PhysicsAlliance Heriot-WattUniversity Edinburgh,UK StefanoLiberati InternationalSchoolforAdvancedStudies FrancescoBelgiorno (SISSA) DipartimentodiMatematica Trieste,Italy PolitecnicodiMilano Milano,Italy SergioCacciatori UgoMoschella DipartimentodiScienzaeAltaTecnologia DipartimentodiScienzaeAltaTecnologia Universitàdell’Insubria Universitàdell’Insubria Como,Italy Como,Italy ISSN0075-8450 ISSN1616-6361(electronic) LectureNotesinPhysics ISBN978-3-319-00265-1 ISBN978-3-319-00266-8(eBook) DOI10.1007/978-3-319-00266-8 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013946369 ©SpringerInternationalPublishingSwitzerland2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Reasoningbyanalogiesisanaturalinclinationofthehumanbrainthatoperatesby associating new and unknown situations to a series of known and previously en- counteredsituations.Onthebasisoftheseanalogies,judgementsanddecisionsare made:associationsarethebuildingblocksforpredictivethought.Itisthereforenat- uralthatanaloguemodelsarealsoaconstantpresenceintheworldofphysicsandan invaluableinstrumentintheprogressofourknowledgeoftheworldthatsurrounds us. It would be impossible to give a comprehensive list of these analogue models butafewrecentandrelevantexamplesareopticalwaveguideanaloguesoftherel- ativisticDiracequation(linkingopticswithquantummechanics),photoniccrystals (linking optical wave propagation in periodic lattices with electron propagation in metals)or,atamoreprofoundlevel,theAnti-deSitter/ConformalFieldTheorycor- respondence(linkingquantumsystemsinDdimensionstogravitationalsystemsin D+1dimensions).Thepurposeofthisbookistogiveageneraloverviewandin- troductiontotheworldofanaloguegravity:thesimulationorrecreationofcertain phenomenathatareusuallyattributedtotheeffectsofgravitybutthatcanbeshown tonaturallyemergeinavarietyofsystemsrangingfromflowingliquidstononlinear optics. Questions often arises regarding the implications of analogue models, particu- larlyinthecontextofanaloguegravity.Sothisappearstopossiblybeagoodstarting pointforaPreface.Theanaloguemodelstreatedherecanallbereconnectedtosome formofflowingmedium.Thisflowingmedium,underappropriateconditionsisex- pected to reproduce or mimic the flow of space generated by a gravitational field. However, it is important to bear in mind that analogue models are always “analo- gies”andnever,orhardlyever,“identities”,meaningthatweshouldnotconfusethe twosystemsundercomparison.Inthespecificcaseofanaloguegravity,theanalo- giesdonotusuallyattempttoreproducethedynamicsofagravitationalsystem,for example a black hole. The dynamics rely on Einstein’s equations and require the presenceofagravitationalsourceterm.Ontheotherhand,theanalogiescanrepro- ducetoalargeextentthekinematicsofablackhole.Thekinematicsreferforexam- pletophotonorparticletrajectoriesandthesearedeterminedbythesystem’sspace- timemetric.Whetherthecurvedspacetimemetricistheresultofagravitationalfield v vi Preface orofaflowingmediumbecomesirrelevantwhentheanalysisisrestrictedtothede- scriptionofwavepropagationandevolutioninthisflowingmedium:thekinematics are identicalandthe analogyis robust.The absenceof a link betweenthe dynam- icsoftheanalogueandgravitationalsystemsmayseemtobeaninherentandeven disappointingweaknessoftheideaspresentedhere.Questionsoftenariseregarding theusefulnessofanaloguemodelsforgravityifwecannotproducepredictionsre- gardingtheevolutionof,forexample,binaryblackholesystems,thequantumorthe purelygeometricalnatureofgravityorwhatevermaybethehottopicatthemoment you are reading this book. These objections are certainly valid: unless things take anunexpectedtwistinthefuture,itseemsratherunlikelythatanaloguegravitywill provideuswithanswerstothesequestions.Thisismainlybecauseanaloguegravity simply does not address these problems. Re-iterating once more, analoguegravity builds upon our knowledge in general relativity and condensed matter physics in ordertobuildadeeperunderstandingofcertainphysicaleffectsthatrelysolelyon the kinematics of the two systems. This declaration contains within it a series of fundamentaland outstanding problems in modern physics that fully justify the in- terestinthefield.Moreover,thesearchforadeeperunderstandingofthelawsthat governtheuniverseisonlyoneaspectofanaloguegravity.Wehopethatinreading this book, you will appreciate how the strive to develop and understand both old andnewanaloguemodelsisleadingtoinnovation,technicaladvancementandnew discoveries in a remarkable range of physical systems ranging from acoustics and gravitywavestooptics,alllinkedbythecommondenominatorthatlieswithinthe geometricaldescriptionofspacetime,asfirstintroducedinthecontextofgravity. So what are these “kinematical” effects addressed by analogue gravity? The most important and obvious member of this list is without doubt Hawking radia- tion.Hawkingradiationisthespontaneousemissionofblackbodyradiationdueto the distortion of the quantum vacuum in the vicinity of a black hole event hori- zon.ThiseffectwasfirstdescribedindetailbyStephenHawkingin1974although thefirsthintsthatblackholesshouldhavenon-zeroequilibriumtemperaturescame fromBekenstein,ayearearlierbasedontheanalogybetweenthelawsofthermody- namicsandthoseofblackholemechanics(yetanotherfruitfulanalogy!).Hawking radiation has since attracted the imagination and efforts of countless scientists, all lookingforadeeperunderstandingofwhythisradiationisemitted,howitisemitted andtheimplicationsofthisemissionwithbigquestionsconcerninginformationloss andeventhefinalfateofouruniverse.Aremarkablepointthatneedstoberemem- beredisthatHawkingradiationinrealisticgravitationalsystemssuchasstellarand galactic black holes, is remarkably weak—so weak that we have very little hope of directly observing it in a gravitational context. This is somewhat of a set-back forwhatiswithoutdoubtoneofthemostfascinatingandprolificideasofmodern physics. Analogue gravity will probably not be able to claim that this unfortunate glitchwillbeovercome,simplybecauseanaloguegravityexperimentsdonotdeal withgravitationalblackholes,yetitcertainlydoesgiveustheopportunitytostudy Hawkingradiationfromafreshandratherunexpectedperspective. BillUnruhfirstproposedananalogueforgravityin1981inthecontextofsound wavespropagatinginaflowingmedium.Theunderlyingideaisverysimple:ifwe Preface vii imagine a sound wave propagating against a counter-flowing medium it is easy to appreciatethatifthemediumflowvelocityissmallerthanthewavevelocity,then thewavewillbeallowedtopropagateupstream.Ifthewavethenencountersave- locitygradientsuchthattheflowacceleratesuptosupersonicspeeds,thenthewave willinevitablyslowdownuntilitiscompletelyblockedbythecounter-propagating medium.Thesoundwavecannotpropagateupstreamagainstasupersonicflow.The wave-blockingpointliesatthetransitionfromsubtosuper-sonicflowand,assuch, representstheanalogueofagravitationalwave-blockinghorizon.Thisisjustapic- torial description of the situation. The mathematics reveals a far more unexpected and revolutionary aspect: the sound wave propagation and trajectory is fully de- scribedbyaspacetimemetricthatisdistortedbytheflowingmediumclosetothe velocity gradient. This distortion can be formally identical to the metric close to theeventhorizonofagravitationalblackholeand,takingonestepfurther,Hawk- ing radiation, now in the form of sound waves is predicted to be emitted from the “sonic”horizon.Mostinterestingly,thesonichorizonemitsHawkingradiationthat dependsonthegradientofthemediumvelocityacrossthehorizonandthereforecan inprinciplebeengineeredandoptimisedinthelaboratory.Forseveralyears these predictionswerenotfullyappreciatedanditwasonlylateronthatBillre-proposed hisideaandtoday,underthethrustofcontinuoustechnologicalimprovementsthere is a thriving and expanding community dedicated to the search of new settings in whichaflowingmediumofsomesortcanbegeneratedandcontrolledinasucha wayastorecreatecurvedspacetimemetricswithvariousapplications. Theresultingtheoreticalmodelsarebecomingevermoresophisticated,spurred by and in turn spurring new laboratory tests and experimental success stories. Hawking-likeradiationmechanismshavenowbeenanalysedinwiderangeofsys- tems well beyond the original acoustical analogue, e.g. superfluids, flowing Bose- EinsteinCondensates,ion-rings,electromagneticwaveguides,soliton-likepulsesin opticalmediajusttonameafew.Thelastfewyearsinparticularhaveseenasud- densurgeofexperimentalteststhatarepavingthewayforgreaterthingstocome: horizons have been generated and observed with gravity waves in flowing water, phononoscillationsinflowingBose-Einstein-Condensatesandlightscatteringfrom laserpulse-inducedflowingopticalmedia.Negativefrequencywaveshavebeenob- served in water-wave and optical analogues and direct evidence of Hawking-like behaviourinaclassicallystimulatedcontexthasbeenobservedusingwater-waves. Thefirstevidenceofspontaneousemissionfromanopticallygeneratedperturbation hasalsobeenobserved.Theseareallremarkablyimportantinlightoftheevidentad- vancementofthewholefieldfromarathersidetrackideatoafullyfledgedresearch area that is leading to innovation and important discoveries at both the theoretical andexperimentallevel. Clearlytherestillremainmanychallengesandhurdles.Notwithstandingthere- markable experimental progress in the last years, a clear and undisputed experi- mentalindicationofspontaneousHawkingemissionisstilllacking.Thismaycome fromoneoftheanaloguemodelsmentionedaboveorpossiblyfromoneofthemany and new models that are currently emerging. An additional point that is requiring significant effort and is one of the main complications with respect to the original viii Preface Hawking description, is the presence of dispersion. On the one hand, dispersion provides a simple solution to the so-called transplanckian problem as it curbs any frequency divergence at the horizon. But on the other hand, it may significantly complicate the analogy or even modify the nature of the emission. This difficulty iscertainlyrelevantintheopticalanaloguesbutplaysarolealsoinothersettings. Moreover,althoughHawkingradiationiscertainlythemostprominentanddesired effectonewouldwanttoobserveintheseanalogues,othereffectsarealsoequally noteworthyandaregraduallygainingattention,suchastheemissionfromanalogues of a cosmological expansion,from superluminal flows, rapidly changing media or from rotating media in analogy with so-called superradiance from rotating black holes. Thescopeofthisbookistopresentanoverviewoftheideasunderlyinganalogue gravity together with a description of some of the most promising and interesting systemsinwhichanaloguesmaybebuilt.Theaimistoprovidescientists,indepen- dentlyoftheirbackgroundinanyofthetopicsapproachedbyanaloguegravity,with ageneralunderstandingofthefield.Afullanddeeperunderstandingwillprobably require some extra work beyond the reading of this book. However, it is our hope thatthesepageswillencourageyoutoponderthebeautyofhowwavepropagation inflowingmediaisintricatelyconnectedtothegeometryofspaceandtimeandto thusstimulatenewideasandnewquestions. Thisbookisdividedintoanumberofchaptersthatstartfromageneraloverview of analogue gravity, providing also some background knowledge to black hole physicsbeforemovingontoconsiderindetailsomespecificanaloguegravitymod- els. Chapter1givesanoverviewofblackholegeometryandHawkingemissionfrom gravitationalandanalogueblackholes. Chapter2deliversanoverviewofthefieldofanaloguegravityasawholewitha briefdescriptionofthefoundationpillarsappliedtoafewspecificexamples. Chapter3givesabroaderdescriptionofsomepossibilitiesforobservingdiverse fundamental quantum effects in the laboratory, therefore going beyond Hawking radiation. Motivatedbyrecentexperimentalsuccess,Chap.4givesatheoreticalandgeneral descriptionofsurfacewavesinfluids. Chapters4to8giveanin-depthdescriptionofsurfacewavesonflowingmediain termsoftheanaloguegravityperspective,roundingupwithadescriptionofrecent experimentalresultsinthisarea. Chapter 9 treats the Bose-Einstein-Condensate analogue model and Chaps. 8 and9treatindetailtheopticalanaloguefirstfromapurelytheoreticalperspective andthenintroducingsomerecentexperimentalresultswiththeseanalogues. Chapters10and11dealwiththeso-calledopticalanaloguemodelincludingan overviewofsomerecentexperimentalresults. Chapter12alsodealswithaparticularapplicationofnonlinearopticsinwhich lightflowsas if it werea fluid(“luminousliquid”)andrepresents a promisingex- perimentalavenue. Chapter 13 gives an overview of Lorentz-invariance breaking and possible ob- servationaltestsinthecontextofanaloguegravity. Preface ix Chapter 14 extends the concepts of analogue gravity to studies involving the topologyofthevacuum—thetopologicalconstraintsonthequantumvacuumstruc- turedeterminesomeuniversalpropertiesofouruniverseandthesecanbemimicked andstudiedinanaloguesystems. Chapter15describesafurtherextensionofanaloguegravity,hereintherealmof Einsteindiffusionmodifiedbyacurved,oranaloguecurvedspacetimebackground. Finally, Chap. 16 is a return to the origins and provides the reader with an overview of the current observational evidence of event horizons in gravitational blackholes. In closing, I wish to acknowledge Fondazione Cariplo for funding and Centro Volta,Como,Italyforhostingthe2011summerschoolonAnalogueGravity—the chaptersinthisbookaremostlybasedonthelecturesdeliveredduringthissummer school.Wealsogratefullyacknowledgealloftheauthorswhosokindlycontributed with their knowledge to this publication and the students and collaborators who kindlyassistedinproof-reading,NiclasWesterberg,MihailPetev,DanielMoss. Edinburgh DanieleFaccio December2012
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