General Relativity: The most beautiful of theories. Applications and trends after 100 years

218 Pages·2015·2.16 MB·English

by  Carlo Rovelli (ed.)

CarloRovelli
GeneralRelativity:TheMostBeautifulofTheories
De Gruyter Studies in
Mathematical Physics
|
Edited by
Michael Efroimsky, Bethesda, Maryland, USA
Leonard Gamberg, Reading, Pennsylvania, USA
Dmitry Gitman, São Paulo, Brazil
Alexander Lazarian, Madison, Wisconsin, USA
Boris Smirnov, Moscow, Russia
Volume 28
General Relativity:
The Most Beautiful
of Theories
|
Applications and Trends after 100 Years
Edited by
Carlo Rovelli
PhysicsandAstronomyClassificationScheme2010
04.20.-q,04.60.-m
Editor
Prof.Dr.CarloRovelli
CentredePhysiqueThéoriquedeLuminy
Aix-MarseilleUniversity
Case907,Luminy
13288Marseille,France
[email protected]
ISBN978-3-11-034042-6
e-ISBN(PDF)978-3-11-034330-4
e-ISBN(EPUB)978-3-11-038364-5
Set-ISBN978-3-11-034331-1
ISSN2194-3532
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Contents
CarloRovelli
Themostbeautifulphysicaltheory|1
AndrewC.FabianandAnthonyN.Lasenby
Astrophysicalblackholes|7
1 Introduction|7
2 Abriefhistoryofastrophysicalblackholes|8
2.1 Earlyhistory|8
2.2 TheSchwarzschildmetric|9
3 Relativisticastrophysicsemerges|11
3.1 Rotatingblackholes|13
3.2 Blackholesasenergysources|13
3.3 MotionintheSchwarzschildmetric|14
3.4 Circularorbits|16
3.5 Stabilityofcircularorbits|17
4 EvidencefromX-rays,quasarsandAGN|20
5 TheblackholeatthecentreoftheMilkyWay|23
5.1 SgrA*|23
5.2 GReffectsonorbits|25
6 Galaxiesandblackholes|29
6.1 AGNfeedback|29
6.2 Jets,Gamma-RayBurstsandthebirthofblackholes|32
7 Currentobservationsofaccretingblackholes|33
7.1 ParticlemotionintheKerrmetric|34
7.2 Currentobservationsofaccretingblackholescontinued|37
7.3 Velocitiesandfrequencies|39
7.4 FurtherAGNproperties|40
8 Measurementsofthemassesofblackholes|41
9 Measurementsofblackholespin|42
9.1 Equationsforphotonmotionandredshift|43
9.2 LightbendingaroundaKerrblackhole|46
9.3 Ironlineemission|46
10 Futureobservationsofastrophysicalblackholes|49
11 Moregeneralsphericallysymmetricblackholes|52
12 Primordialblackholes|54
12.1 Hawkingradiation|54
12.2 Linkwithsurfacegravity|55
12.3 Astrophysicalaspectsofblackholeevaporation|56
VI | Contents
12.4 Blackholeentropy|57
12.5 LawsofblackholethermodynamicsandthePenroseprocess|58
12.6 Adiabatic(reversible)changes|60
12.7 Otherprocessesforextractingenergyfromaspinningblack
hole|60
13 Conclusions|62
GeneG.Byrd,ArthurChernin,PekkaTeerikorpi,andMauriValtonen
ObservationsofGeneralRelativityatstrongandweaklimits|67
1 Introduction|67
2 Testsinthesolarsystemandbinarysystems|69
2.1 Orbitprecession|69
2.2 Gravitationalwaves|70
2.3 Lense–Thirringeffectandrelativisticspin-orbitcoupling|71
2.4 Bendingoflightraysandgravitationalredshift|71
2.5 Massivespinningblackholetest|72
3 Observationaldiscoveryofanon-zerocosmologicalconstant(dark
energy)|73
4 Weaklimittestnearzerogravitysurface|74
4.1 DarkenergyantigravityasatestofGeneralRelativity|74
4.2 Localdarkenergytestviaoutflow|74
4.3 Dynamicalstructureofagravitatingsystemwithindarkenergy|77
5 Estimatingcosmologicallynearbydarkenergy:theLocalGroup|79
6 Mass,darkenergydensityandthelostgravityeffect|81
7 DarkenergyintheComaClusterofgalaxies|82
8 TestingtheconstancyofΛ|82
9 Stronglimit:Spinningblackholesandno-hairtheorem|85
10 OJ287binarysystem|87
10.1 Thebinarymodel|87
10.2 OJ287flaresandjet|88
10.3 OJ287orbitparameters(withoutusingoutbursttimes)|92
11 ModelingbinarieswithPostNewtonianmethods(withoutburst
times)|94
12 OJ287resultsatthestrongfieldlimit|94
13 Conclusions|95
14 Appendedsection;mass,darkenergydensityandthe“lostgravity”
effect|97
15 Appendedsection:darkenergyintheComaclusterofgalaxies|101
15.1 Threemassestimatesofthecluster|101
15.2 Mattermassprofile|102
15.3 Upperlimitsandbeyond|104
16 Appendedsection:modelingbinarieswithPostNewtonian
methods|105
Contents | VII
IgnazioCiufolini
GeneralRelativityanddraggingofinertialframes|125
1 Frame-dragging:thetheory|126
1.1 Draggingofinertialframesandtheoriginofinertia|126
1.2 Draggingofinertialframesandthegravitomagneticanalogy|127
1.3 ThegravitomagneticformalanalogyofGeneralRelativitywith
electrodynamics|128
1.4 Draggingofinertialframesinsideahollowsphere|131
1.5 Frame-draggingphenomenaonclocksandphotons|132
1.6 Frame-dragging,time-delayandgravitationallensing|134
1.7 [Aninvariantcharacterisationofframe-dragging]|138
2 TheneedtofurthertestGeneralRelativity|140
2.1 TheuniverseandthetriumphGeneralRelativity|140
2.2 Theriddleofdarkenergyanddarkmatter|141
2.3 Unifiedtheories,alternativegravitationaltheoriesandsomelimitsof
GeneralRelativity|141
2.4 [Frame-dragging,Chern–SimonsgravityandStringtheory]|142
3 TheholygrailofexperimentalGeneralRelativityanditsobservation
withtheLAGEOSsatellitesandGravityProbe-B|145
4 TheLARESspaceexperiment|151
4.1 TheLARESsatellite,itsstructureanditsorbit|151
4.2 TheLARESsatellite,GeneralRelativityandgeodesicmotion|153
4.3 TheLARESsatelliteanditspreliminaryorbitalresults|154
4.4 [LARESerroranalyses]|155
5 Conclusions|158
NeilAshby
GNSSandotherapplicationsofGeneralRelativity|165
1 Introduction|165
2 Relativityprinciples|169
3 Astronomicalandgeocentrictimescales|170
4 Earth-basedtimescalesTT,TAI,UTC|174
5 Gravitationalfrequencyshifts|176
6 Sagnaceffect;realizingcoordinatetime|178
7 Relativisticeffectsonorbitingclocks|180
8 Theeccentricityeffect|183
9 Navigationontherotatingearth|183
10 Emissioncoordinates|186
11 JUNOandothermissions|187
12 Summary|187
VIII | Contents
CarloRovelli
Thestrangeworldofquantumspacetime|189
1 Aworldwithnospace|189
2 Aworldwithouttime|191
3 Loopgravity|194
4 Quantumspacetime|198
5 Empiricalevidence|198
Index|203
Listofcontributors|209
CarloRovelli
The most beautiful physical theory
“Themostbeautifulofallexistingtheories.”
LandauandLifshitz
“Probablythegreatestscientificdiscoverythatwasevermade.”
Dirac
“Scarcelyanyonewhofullyunderstandsthistheorycanescapefromitsmagic”
Einstein
(AllquotedinS.Chandrasekhar,J.Astrophys.Astr5(1984),3–11.)
Therearemasterpiecesthatmoveusdeeply:Mozart’sRequiem,theOdyssey,theSis-
tineChapel,KingLear....Theygivesusneweyestoseetheworldfromanoveland
deeperperspective.Generalrelativity,thejewelofAlbertEinstein,isoneofthese.
Conceivedalmostinisolation,withoutasingleelementofnewempiricaldata¹,
basedonanacutereflectiononthescientificknowledgeavailableatthetimeandon
thecourageofchallengingcommonsensefrontally,generalrelativityisjustasimple
ideaandafewlinesofequations.Butanastonishingwealthofincrediblepredictions
followfromthese:timerunsfasteronthemountainsthanatseaside;lightdoesnot
travelinstraightlines;space-timebends,andcantrembleoverthevastinterstellar
landslikethesurfaceofalakeunderasoftwind;itcanbendovertheweightofastar
tothepointofcollapsingintoaholewhereallthingsandevenlightcanenterbutnot
comeout;theentireuniversecannotstayput,butmustcontractorexpand,andin
factisbornfromafiercelyhotconcentratedcore....
Allthissoundslikeataletoldbyanidiot,fullofsoundandfury,morethansober
resultsofphysicists’scalculation.AndmuchofthiswasstillseenassuchwhenIstud-
iedattheuniversity.StevenWeinberg’s1972generalrelativitytextbookstillcallsthe
blackholes’s horizons “hypothetical” and says that r = 2m Schwarzschildradius
“doesnotseemtohavemuchrelevancefortherealworld”(page207)!
Instead,ithasallcometrue.Theuniversehasturnedouttobetrulysokaleido-
scopic: one after the other, years after year, all the astonishing predictionsderived
fromthetheoryhavebeenconfirmedbyobservations.
Todaywemeasurethedifferenceoftherateatwhichtimeflowsatafewdecime-
tresofelevationdifference;theevidenceforblackholesisoverwhelming;theevidence
forgravitationalwavesisindirect,butverystrong;nobodyquestionsanymoretheidea
thattheuniverseexpandsandhasevolvedfromahotanddensecore...Physicsisnot
1 Thereareotherexamplesofthis:Copernicus,forinstance.
CarloRovelli:CPT-CNRS,Case907,Luminy,13288Marseille,France
2 | CarloRovelli
newtospectacularpredictions:Newton’s theory hasbeenused todeducetheexis-
tenceofNeptunebeforeseeingit,Dirachaspredictedantimatter,Maxwelltheelec-
tromagnetic waves, the standard model of particlephysicshas predicted the Higgs
particle,andsoon.Butnotheoryhaspredictedasequenceofpreviouslyunconceiv-
ableaspectsofrealitylikegeneralrelativity.
IremembermyemotionwhenIbeganunderstandingsomethingaboutthetheory.
Itwassummer.IwasonabeachinCalabria,immersedintheMediterraneanglare,
perfumingofancientGreece,atthetimeofmylastuniversityyear.Holidaysiswhen
onestudiesbetter,withouttheschool’sdistractions.Istudiedonabookgnawedby
mice;Ihadusedittoblocktheholesoftheselittlecreatures,atnight,inthehippy
houseontheUmbrianhillwhereIusedtotakerefugefromtheboredomofUniversity
lectures.Everyonceinawhile,Iraisedmyeyesfromthewornoutbook,tostarethe
sparkleofthesea:Icouldalmostseethebendingofspaceandtime.Itwaslikemagic,
asasoftfriend’svoicewhisperinganextraordinarysecrettruthatmyear,aveilbeing
movedfromreality,revealinganewglimpseofitshiddenbeauty.
SincewelearnedthattheEarthisroundandspinning,wehaverealisedthatre-
alityisnotasitappears:everytimeweunderstandanewpieceofit,isanemotion.
Anotherscreenthatfalls.Butamongallthemanyleapsforwardinourknowledge,
oneaftertheotherinthecourseofhistory,theonemadebyEinsteinfrom1907to1915
isprobablyaleapwithoutequals.
Foronething,thetheoryisofbreathtakingsimplicity.Newtontriedtoexplainwhy
thingsfallandplanetsrevolve. Heimagineda“force”thatpullsbodiestowardone
another.Howcouldthisforcepullthingsfarawayfromeachother,withoutanything
actinginbetween,wasquiteunclear,andthefatherofsciencecautiouslydidn’tfeign
hypotheses.Healsoimaginedthatbodiesmoveinspace.Thenatureofsuch“space”,a
sortof“container”oftheworld,whichNewtondidfeign,wasnotcleareither.Butafew
yearsbeforeAlbert’sbirth,FaradayandMaxwellhadaddedaningredienttoNewton’s
cold universe: the electromagnetic field,a realentity fillingspaceand carryingthe
electricforce.Einstein,fascinatedfromchildhoodbytheelectromagneticfield,that
pushedtherotorsofthepowerplantsbuiltbyhisfather,soonrealisedthatgravity,
likeelectricity,hadtobecarriedbyafield.Andherecametheextraordinaryidea:the
gravitationalfieldisnotwidespreadinspace:thegravitationalfieldisspace.
ThestrangeentitythatNewtonhadintroducedintophysics,“space”,²isunder-
stoodtobenothingelsethanaconfigurationofthegravitationalfield.Andtheentity
that“carriesalong”theforceofgravity,liketheelectromagneticfieldcarriestheelec-
tricforce,isspaceitself,whichistosay,thegravitationalfield.Thetwoconceptual
puzzlesofNewtonianismsolveoneanother.Thisisthesimpleideathatgroundsthe
theoryofgeneralrelativity.
2 Cartesianphysicshadnothingofthesort:extensionwasapropertyofthingsand“space”wasjust
arelationbetweenthings,so“emptyspace”wasalogicalimpossibility.