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Chapter 4 Gravitational waves（第1页）

Chapter4Gravitationalwaves

Gravitationalwaveshavealreadybeeioned，inChapter3。’ssiderthemiail。YouwillreChapter1that，iheravityisduetothecurvatureofspace-time。Massiveobjectslikestarsasdeformtheshapeofthespawhichtheyexist，sothatotherbodiesthatmhitappeartohavetheirtrajectoriesbent。Itisthemistakeioionofthesebodiesasinaflatspacethatleadsustoihereisaforcecalledgravity。Infact，itisjustthecurvatureofspace-timethatisatwork。

Therelevahisfravitatioifagroupofmassivebodiesareiion（sutheSolarSystem，orinabinarypulsar），theureofthespawhichtheyexistisnotusuallyfixedihecurvatureofthespace-timeissetbythemassivebodies，soifthebodiesareinmotioureofspace-timeshouldbeexpectedtobetlyg。Thestificwaytodescribethissituationistosaythat，iheory，space-timeisadyy。

Asahis，siderthesuperwediscussedpreviously。Beforetheircorescollapse，leadingtocatastrophicexplosion，theyarerelativelystableobjects，muchlikeourownSun。Inthisstageoftheirlifetheyshouldthereforebeexpectedtocurvethespace-timearouhesamewaythattheSundoes，andshouldthereforehaveasimilargravitatioertheyexplodetheysettledowarorablackhole，andonreturivelystablestate，withagravitatiodoeshtime。Duringtheexplosioheyejecthugeamountsofmassaheirgravitationalfieldgesrapidlythroughoutthisprodthereforesodoesthecurvatureofthespace-timearoundthem。

&emthatispushedoutofequilibriumaogerapidly，thiscausesdisturbaheformofwaves。Amoredoleofawaveisehrowastooapreviouslystillpoerinthepondwasinitiallyie，butthestonecausesarapidtheamouohewateririestoreturntoitstranquilinitialstate，whichresultsiiourbaheformofripplesthatmoveawayfromthepoionelanded。Likewise，aloudnoiseinapreviouslyquietrinatesfromaairpressureatapoiereospeaker）。Thedisturbaheairpressurepropagatesoutressurewaveastheairtriestoreturntoastablestate，ahesepressurewavesassound。

Soitiswithgravity。Ifthecurvatureofspace-timeispushedoutofequilibrium，bythemotiony，thenthisdisturbawardsaswaves。Thisisexactlywhatoastarcollapsesanditsoutereedbythesubsequentexplosioprocessthatothestarcausesadisturbaureofspace-time，muchlikethestonefallingintothepourbaer。Andagain，justasintheexamplesjustgiveurbaesoutwardsas

Thespeedavespropagateusuallydepehroughwhichtheytravel。Forexample，weknowthatsouravelslightlyfasterinwarmairthantheydoincoldair。Themediumfravitationalace-timeitself，andagtoEiheory，theypropagateatexactlythesamespeedaslight。Justaswithlight，theyarealsoexpectedtohaveaspeedthatisihemotionofthepersohem，andthatisihemotionoftheirsource。Theytherefateinformationatthemaximumpossiblespeed，asnothingtravelfasterthanlight。

&ofagravitational>

Totryandmakeseagravitatiomightbeusefultosiderwhatitsefectsshouldbeonagroupofobjectsasitpassesthroughthem。Forexample，ifytodescribetheondtoanalienwhowasn’tfamiliarwithwater，youmightstartbysuggestingthattheefectofthewaveistomaketheliliesonthesurfaceofthepondmoveupanddowninasmooth，repetitiveway。Letussiderthedingsituationwithgravitational>

&bygauniformcloudofgas’oatingihisremovestheefectoftheEarth’sowngravitationalfield，whiytimesstrohananygravitatioweareeverlikelytosee，aswellasremovinganydisturbahegasmightfeelfrwithahegravitatioravelsthroughthecloudofgas，asihentheprihewaveistodisplacethegasirasdireation。Thatis，ifthewavetravelsfromlefttht，theithegasaredispladdown，andinandoutoftheplahepage。

&hegravitatioheayinitiallymakeitlookalittlebitlikethewaveisbeingsupportedbythegasitself，muchlikethewaveinthepondissupportedbythewater。Itis，however，quitediferent。Withthegravitatioisspace-timethatcarriesthewave。Theefectofthegravitatiohegasistherefoustotheefectthatthewaterwavehasonalilythatsitsonthesurfaceofthepohewateriself。Thatis，thegravitatioawaveiratherapropagatingdisturbaimeinwhichthegasexists。

8。Anillustrationofaassingthroughacloudofgas。Thewavetravelsfromlefttht，anddisplacestheparticlesofgasup-and-down，andin-and-outoftheplahepage。

Infact，whatthegravitationalwaveisreallydoinginthisexampleisgtheamountofspacethatexistsihataretrasdireatioalthoughtheatomsinthegasmightbeclether（orfurtherapart）thantheywerebeforetheassedthroughthem，itisheatomshavemoved，butbecausetheamountofspathemhasbeendecreased（orihewave。Thegravitationalwavegesthedistasbyalteringhowmuchspacethereisihem，notbymovihinafixedspace。Thisisonlypossiblebecauseofthefactthatspaotfixediheorybutisitselfdynamical。

Tosidertheefectsofgravitationalwavesiusnowsideraringofpartidthinkwhatentifagravitatiohroughit。ThisisillustratedinFigure9，whereinthiscasethegravitationalwaveisbeiobeingupwards，outoftheplaheefectofthewaveisohedirestrasdireatiofpartitheplahepageshiveusaprettygoodideaofitsces。

9。Thedeformationthataringofparticleswouldexperienceifagravitatiohroughit，inanupwardsdire（i。e。iofthepage）。Theleftmostimageshowstheinitialfiguratioherimages（fromlefttht）shatfoursubsequentiime。

Iftheparticlesareinitiallyarrangedidarenotattaythiher，thehewavewillbetopresstheoionaiheresultisthattheparticlesstarttoformaheassesthrough，itstretchesthecirclesmoothlyuntilitreachesamaximumdeformation，atwhititstopsaheprotilthedirewhiitiallystretchedisataminimum。ThisstretdsquashidiresisillustratedinFigure9，anduesuntiltheassed。

Theissionofgravitationalwaveshasalreadybeehebinarypulsar。Thewavesergyawayfromthesystem，sothatthetwoarsslowlytowardseachother。Themeasuredrateofin-spiralinthebinarypulsarhasgivengoodevideheexistenceofgravitatioisofgreatstifiteresttotryasofthesewavesdirectlyaswell。Thiswasdoimeiember2015bytheLIGOexperimedeteofgravitatioicularlyexgbecauseitprovideuswithairelyoviewtheUhefirsttime，wedoorelyonlighttoseedistasasweowlookatthemthrravitationalfieldsdirectly。Thisallowsustoseeens，forexample，whenblackholescollide。

&deteofgravitationalwavesalsoallowsforestsofEiheravity。Ingeneral，oneberofdiferentpossibleefeapassinggravitationalwave。Forexample，theareaofthecircleofpartiFigure9couldhavebeeherecouldbedeformationsofspagthedireationofagravitationalwave（aswellasintraions）。Itistheequatioeihecurvatureofspadtimethatforbidsthesepossibilitieswithiifhewaswroheycouldbethereinnature。ByusislikeLIGO，welooktoseeifgravitatiohespecificefectsthatEihisprovidesyetaofhistheory。Beyondthis，beiogainanehathappenswhenblackholescollideprovidesanumberofexgpossibilitiesforthefurtherstudyofgravitationalphysics。

Gravitatioore

&enceofgravitationalredictedbyEinsteinin1916，and，afternearlyaturyofefort，theyweredetectedforthefirsttimein2015。Thereasonittooksolongtodothisislargelyaceoftheextremelylolitudeofthesignal。Inthediagramshowniheefectofthegravitationalwaveswasenormouslyexaggeratediryaeasiertovisualizetheirefereality，the’usintheshapeshouldoobeatthelevelofaboutoinahundredmilliontrillion。Thatis，ifwemadearingofparticlesthatwasa1，000kmacross，weshouldsshapetogebymorethanatrillionthofatimetre。Thisisobviouslyverydiculttodetect。

&hediculty，orperhapsbecauseofit，ahugeamouhasbeeryiatioly。MuchoftheearlyhistoryofthisworkiarenowcalledWeberbars。Theseis，erJosephWeberoftheUyofMaryland，sistededersofmetal。Theywereaboutametrele。TheideawasthatifagravitatiohroughtheEarth，ahroughthedeteitmightcausethebart，likeabellhitbyahammer。Forthistohappeioobeofjusttherightfrequency。Ifsuchawaveweretoexist，itshouldbeexpeallvibrationsinthebar。

&orsthatwereusedtoseeifthebarwasvibratiiveenoughtodetegesihof1partin1，000trillion。Remarkablysehisis，it’sravitatiotoexist。Thisdidn’tstopafewfalsealarmsbeihough。In1968，WeberclaimedhehadevideheexistenceofgravitationalouldhavemadehimaprimederforaNobelPrize。Uheclaimeddete’tbereproduditisnowwidelybelievedthatitwaserroneous。

SomemodernversionsoftheWeberbararestillbeioday。AheMiisistsofa1，150kgmetalsphere，andisabout1，000timesmoreseheonesusedbyWeberhimself。However，mostmoderdeteggravitationalwavesuseadiferentteology，knowry。Detectorsbasedonthisteologyaresimilar，inpriheMiorleydevicedesChapter2。Themoderndevicesare，however，much，muchlarger。Thelargestofall，atthetime，istheLIGOdetetheUSA。

LIGO，ortheLaserIerGravitatioory，hasteration;oneisinLivingston，Louisiana，aherisinRid，Washiesagiaer。Theierssistoftwo‘arms’，whicharebuilttlestoeachother，asillustratedinFigure6。Eacharmisseveralkil，andsatubeofnearvaetrewide。Lasersarefireddowhesetubes，aedfromhangiheendofeathelaserlightmakesitswaybacktothepoihearmsmeetitbestudied，ahofeasihepatterhetwolaserbeamsi。Whenagravitatiohroughthem，thearmlengthsdthepatterheiialsoge。

&ectorisexquisitelyacdhasasensitivitythatisaboutamillioerthaheteicalgesrequiredtoreachthisaccuracyarepheheexperimentalistshavehadtoovereallkindsnalsthatpollutethedata。Theserangefromseismioise，inwhiyiiohcausethere’egobjectstovibrate，tothevibratiorongwi，thedetectorsarenowbeioingfactorsistlythefactthatlaserlightismadeupfromphotons，sothatauoussignalfrobjeotpossible。

&hesegreatproblems，aheenormousfinancial，politidengineeringdicultiesithastakehem，theLIGOdetectorhasultimatelybeesu14September2015itdetected，forthefirsttimeinhumanhistory，direcefortheexistenceofgravitationalwavesfromgblackholes。It’salmostimpossibletooverstatethesighisevent，whichwillprobablygodowninhistoryasostificatsoftheme。Solet’ssideritiail。

&ionofgravitationalwavesbyLIGO

Atprecisely45sedspast9:50a。m。（Greeime），oember2015，theLIGOgravitatiooratLivingston，Louisiaedafluierferometer。Thissignallastedforonly0。2sedappearedtomakethe4km-longarmsoftheiriergthbyabout11，000thewidthofproton。About0。007sedslater，asimilarsigedbythedeteHanford，Washingtoalarmbellsringing，aistserimentweresooniheyhaddetectedagravitationalassingthroughtheEarth。

&hinkabouttheeventthatcausedthewave，let’ssiderthesignalitself。IfyouweretolookatthedatafrOsite，itearaslittlemorethanabliponthebackoftheoisethatexistswithihesignal，atitspeak，wasolitudeoftherapollutesthedetectors’output。Thismakesitdiculttosee，anddiitasatruedete。Thereasoistsweresoceditreallywasagravitatiowofold。First，thewobbleiectors，atthetwodiferentlos，wereverysimilar。Itmightbepossibletohavearaoioethingthatlookedlikeagravitatioohaveexactlythesametremoratalmostthesametimeattwraphisishighlyunlikely。Sedjustasimportantly，theLIGOstistskshapethewaveshouldtake。Thisallowedthemtosthedata，inaproatchfiltering，tolookfnal。TakisintoaeansthattheLIGOstistsaremorethan99。999perfidentthatthewobblestheyobservedreallywereduetoapassinggravitatiotoanyspurioussouroise。

ThisresultisenormousatfortheexperimeLIGO，whoprodudoperatedtwoofthemostsensitivepiecesofstifitthathaveeverexisted。Itis，however，alsoahugeatfeheoreticalphysicists。Thisisbecausethematchfilteriionedbefore，andwhichiscrucialforthedete，requiresthedetailedmodellihemravitationalfieldsinnature:mergingblackholes。ItisonlybyuaailsofenswhenblackholescollidethatstistsroducefiltersfortheexpectedgravitationalwavesignalsthatLIGOmightdetedthisisalotmorediitsounds。Thereareanumberofdiferentwaysthattwoblaerge，andanawfullotofmathematiputationalworkhasbeeoualywhatEiheorypredictsfravitatioshouldbeemittedfromsuchsystems。

Iwon’tgoiailsofaics，butweshouldsidertheactualastrophysitthatledtotheemissionofthewaves。Fromtheshapeofthesigors，aailedmodellingblackholesdescribedearlier，itisthoughtthatthewaveswerecreatedbytwoblackholesthatspiralledtowardseachotherbeforeeventuallymergilingdowntoformeblackhole。Thetwoblackholesthatcametogetherinthissariowerearouy-hirty-sixtimesthemassoftheSuleddowntoafieinwhichtheresultingblackholewasaboutsixty-twotimesthemassoftheSun。Thismightsoundratherpeaceful，butit’saeofthemostvioleoature。

&ereaderwillwehirty-sixdoesy-two。Thisisbecausethegravitatioedduringthemergercarriedaway3solarmassesy（rememberthatE=msteihisisaraordinaryamountyforasystemtolose，andgoessomewaytwhyitshouldbethoughtofasavioleogivesomeber，siderthefollowiwoblackholeswereemittinggravitatioheyweregivingythaarsintheobservableuogether。Theywerealsoobservablefrom1。3billionlightyearsaway，whichisasizablefraoftheentireobservableuhen，wasaveryextremeevent，andahighlyexthepointofviewofgravitationalphysicists。

Futureprospects

Althoughgravitationalwaveshaveed，there’snoreasonforustorestonourlaurels。ThedetebyLIGO，aswellasbeingtheendofalo，isalsothestartofaroofthereasonforthishopefulstatementisthatLIGOwill，withanyluuetodeteoreoftheseevents。Another，however，isduetotheionofgravitatioorsthatisbeingplannedandbuilt。ThisihepossibilityofbuildingaLIGOsiteoutsideoftheUSA，withIhetfavouredloextrasiteofthistypewouldiheabilityofLIGOtodetermiionontheskyfromwhichagravitatioed，andhenceimprovetheprospeggravitationalwavesasaastronomywithoutlight。

BeyondLIGO，anotherpossibilityforthefuturedeteofgravitationalrojectcalledeLISA（theEvolvedLaserIerSpaa）。TheeLISAmissionisaEuropeanSpacyproposaltocreateadetespace。ThisbriaisoverEarth-basedgravitatioors，theforemostofwhichisthatitwouldbeimmuoseismioise。Thismeansitwouldbeseeoffrequeisextremelyhardtodetetheground。Ituchlargerthah-baseddetectors，asthelaserssimplybefiredbetweees，rotectivehousing。TheproposalforeLISAistocreateatriangleoflaserbeamsbetweesatellites，eachofwhichisseparatedfromtheothersbyafewmilliores。Wheogravitatioerisbetter’soeLISAisagreatprospectforfuturedetes。

ButwhilethearmlengthsofeLISAbehuge，andtheseismioiseispletelyabsesowheeinspaceis，butisy。

ThechargedmaterialthattheSunthrowsofshouldbeexpeterfereace-baseddetectorofthiskind，asshouldtheicraysthatbardtheEarth。OnthegroundweareshieldedfromthisiheEarth’satmagravitatioorinspaotbe。And，ofcourse，itismuchmorediicultteandmaiwhenit’siheless，therearehighhopesthateLISAwillbebuilt，andthatitwilldetectgravitationalace。

&herwayinwhichgravitatiobedetethefutureisusingologicalobservables。ologyisthestudyofthestateaionoftheUniverseasawhole，andtherearesiderableprospectsfthefisofgravitationalwavesinanumberofupissions。WewilldiscusstheseiailinChapter5。