General Relativity Today

arXiv:0704.0754v1[gr-qc]5Apr2007GeneralRelativityToday∗†ThibaultDamourInstitutdesHautesEtudesScientifiques35routedeChartres,91440Bures-sur-Yvette,FranceAbstract:Afterrecallingtheconceptualfoundationsandthebasicstruc-tureofgeneralrelativity,wereviewsomeofitsmainmoderndevelopments(apartfromcosmology):(i)thepost-Newtonianlimitandweak-fieldtestsinthesolarsystem,(ii)stronggravitationalfieldsandblackholes,(iii)strong-fieldandradiativetestsinbinarypulsarobservations,(iv)gravitationalwaves,(v)generalrelativityandquantumtheory.1IntroductionThetheoryofgeneralrelativitywasdevelopedbyEinsteininworkthatextendedfrom1907to1915.ThestartingpointforEinstein’sthinkingwasthecompo-sitionofareviewarticlein1907onwhatwetodaycallthetheoryofspecialrelativity.RecallthatthelattertheorysprangfromanewkinematicsgoverninglengthandtimemeasurementsthatwasproposedbyEinsteininJuneof1905[1],[2],followingimportantpioneeringworkbyLorentzandPoincar´e.Thetheoryofspecialrelativityessentiallyposesanewfundamentalframework(inplaceoftheoneposedbyGalileo,Descartes,andNewton)fortheformulationofphysicallaws:thisframeworkbeingthechrono-geometricspace-timestructureofPoincar´eandMinkowski.After1905,itthereforeseemedanaturaltasktoformulate,reformulate,ormodifythethenknownphysicallawssothattheyfitwithintheframeworkofspecialrelativity.ForNewton’slawofgravitation,thistaskwasbegun(beforeEinsteinhadevensuppliedhisconceptualcrystallizationin1905)byLorentz(1900)andPoincar´e(1905),andwaspursuedintheperiodfrom1910to1915byMaxAbraham,GunnarNordstr¨omandGustavMie(withtheselatterresearchersdevelopingscalarrelativistictheoriesofgravitation).Meanwhile,in1907,Einsteinbecameawarethatgravitationalinteractionspossessedparticularcharacteristicsthatsuggestedthenecessityofgeneralizingtheframeworkandstructureofthe1905theoryofrelativity.Aftermanyyearsofintenseintellectualeffort,Einsteinsucceededinconstructingageneralized∗TalkgivenatthePoincar´eSeminar“GravitationetExp´erience”(28October2006,Paris);toappearintheproceedingstobepublishedbyBirkh¨auser.†TranslatedfromtheFrenchbyEricNovak.1theoryofrelativity(orgeneralrelativity)thatproposedaprofoundmodificationofthechrono-geometricstructureofthespace-timeofspecialrelativity.In1915,inplaceofasimple,neutralarena,givenapriori,independentlyofallmaterialcontent,space-timebecameaphysical“field”(identifiedwiththegravitationalfield).Inotherwords,itwasnowadynamicalentity,bothinfluencingandinfluencedbythedistributionofmass-energythatitcontains.Thisradicallynewconceptionofthestructureofspace-timeremainedforalongwhileonthemarginsofthedevelopmentofphysics.Twentiethcenturyphysicsdiscoveredagreatnumberofnewphysicallawsandphenomenawhileworkingwiththespace-timeofspecialrelativityasitsfundamentalframework,aswellasimposingtherespectofitssymmetries(namelytheLorentz-Poincar´egroup).Ontheotherhand,thetheoryofgeneralrelativityseemedforalongtimetobeatheorythatwasbothpoorlyconfirmedbyexperimentandwithoutconnectiontotheextraordinaryprogressspringingfromapplicationofquantumtheory(alongwithspecialrelativity)tohigh-energyphysics.Thismarginaliza-tionofgeneralrelativitynolongerobtains.Today,generalrelativityhasbecomeoneoftheessentialplayersincutting-edgescience.Numeroushigh-precisionex-perimentaltestshaveconfirmed,indetail,thepertinenceofthistheory.Generalrelativityhasbecomethefavoredtoolforthedescriptionofthemacroscopicuni-verse,coveringeverythingfromthebigbangtoblackholes,includingthesolarsystem,neutronstars,pulsars,andgravitationalwaves.Moreover,thesearchforaconsistentdescriptionoffundamentalphysicsinitsentiretyhasledtotheexplorationoftheoriesthatunify,withinageneralquantumframework,thedescriptionofmatterandallitsinteractions(includinggravity).Thesetheo-ries,whicharestillunderconstructionandareprovisionallyknownasstringtheories,containgeneralrelativityinacentralwaybutsuggestthatthefunda-mentalstructureofspace-time-matterisevenricherthanissuggestedseparatelybyquantumtheoryandgeneralrelativity.2SpecialRelativityWebeginourexpositionofthetheoryofgeneralrelativitybyrecallingthechrono-geometricstructureofspace-timeinthetheoryofspecialrelativity.ThestructureofPoincar´e-Minkowskispace-timeisgivenbyageneralizationoftheEuclideangeometricstructureofordinaryspace.Thelatterstructureissum-marizedbytheformulaL2=(Δx)2+(Δy)2+(Δz)2(aconsequenceofthePythagoreantheorem),expressingthesquareofthedistanceLbetweentwopointsinspaceasasumofthesquaresofthedifferencesofthe(orthonormal)coordinatesx,y,zthatlabelthepoints.ThesymmetrygroupofEuclideange-ometryisthegroupofcoordinatetransformations(x,y,z)→(x′,y′,z′)thatleavethequadraticformL2=(Δx)2+(Δy)2+(Δz)2invariant.(Thisgroupisgeneratedbytranslations,rotations,and“reversals”suchasthetransformationgivenbyreflectioninamirror,forexample:x′=−x,y′=y,z′=z.)ThePoincar´e-Minkowskispace-timeisdefinedastheensembleofevents(ide-alizationsofwhathappensataparticularpointinspace,ataparticularmoment2intime),togetherwiththenotionofa(squared)intervalS2definedbetweenanytwoevents.Aneventisfixedbyfourcoordinates,x,y,z,andt,where(x,y,z)arethespatialcoordinatesofthepointinspacewheretheeve