《1971 碰撞黑洞的引力辐射-精品文档资料整理.pdf》由会员分享，可在线阅读，更多相关《1971 碰撞黑洞的引力辐射-精品文档资料整理.pdf（3页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、VOLUME26,NUMBER21PHYSICALREVIEWLETTERS24Mwv19710Permanentaddress:InstituteforAtomicPhysics,Bucharest,Rumania.See,e.g.,G.A.Keyworth,G.C.Kyker,Jr.,E.G.Bilpuch,andH.W.Newson,Nucl.Phys.89,590(1966).M.Maruyama,K.Tsukada,K.Ozawa,F.Fujimoto,K.Komaki,M.Mannami,andT.Sakurai,Nucl.Phys.A145,581(1970).W.M.Gibso
2、n,M.Maruyama,D.W.Mingay,J.P.F.Sellschop,G.M.Temmer,andR.VanBree,Bull.Amer.Phys.Soc.16,557(1971).G.M.Temmer,M.Maruyama,D.W.Mingay,M.Petrascu,andR.VanBree,Bull.Amer.Phys.Soc.16,182(1971).L.H.Goldman,Phys.Rev.165,1203(1968).W.Darcey,J.Fenton,T.H.Kruse,andM.E.Will-iams,unpublished.R.VanBree,unpublishedc
3、omputerprogrambasedinpartonB.TeitelmanandG.M.Temmer,Phys.Rev.177,1656(1969),Appendix.Thisprogramdoesnof;allowforidenticalspinsandparities,andthefitisthereforeverytentative.J.R.Huizenga,privatecommunication.Thisre-presentsthebestestimate,usingaslightextrapola-tionfromtheobsemedneutron-capture2+-level
4、den-sityat7.6-MeVexcitation.N.Williams,T.H.Kruse,M.E.Williams,J.A.Fenton,andG.L.Miller,tobepublished.H.Feshbach,A.K.Kerman,andR.H.Lemmer,Ann.Phys.(NewYork)41,280(1967);R.A.FerrellandW.M.MacDonald,Phys.Rev.Lett.16,187(1966).IntermediateStctheinNuclearReactions,editedbyH.P.KennedyandR.Schrils(Universi
5、tyofKentuckyPress,Lexington,Ky.,1968).J.D.Moses,thesis,DukeUniversity,1970(unpub-lished).3D.P.Lindstrom,H.W.Newson,E.G.Bilpuch,andG.E.Mitchell,tobepublished.J.C.Browne,H.W.Newson,E.G.Bilpuch,andG.E.Mitchell,Nucl.Phys.A153,481(1970).5J.D.Mosey,privatecommunication.L.Meyer-Schutzmeister,Z.Vager,R.E.Se
6、gel,andP.P.Singh,Nucl.Phys.A108,180(1968).YJ.A.Farrell,G.C.Kyker,Jr.,E.G.Bilpuch,andH.W.Newson,Phys.Lett.17,286(1965).J.E.MonahanandA.J.Elwyn,Phys.Rev.Lett.20,1119(1968).GravitationalRadiationfromCollidingBlackHolesS.W.HawkingInstituteofTheoreticalAstronomy,UniversityofCambridge,Cambridge,England(Re
7、ceived11March1971)Itisshownthatthereisanupperboundtotheenergyofthegravitationalradiationemittedwhenonecollapsedobjectcapturesanother.Inthecaseoftwoobjectswithequalmassesmandzerointrinsicangularmomenta,thisupperboundis(2-W2)m.Weberhasrecentlyreportedcoincidingmea-surementsofshortburstsofgravitational
8、radia-tionatafrequencyof1660Hz.Theseoccuratarateofaboutoneperdayandtheburstsappeartobecomingfromthecenterofthegalaxy.Itseemslikely4thattheprobabilityofaburstcausingacoincidencebetween%ebersdetectorsislessthan,.Ifoneallowsforthisandassumesthattheradiationisbroadband,onefindsthattheenergyfluxingravita
9、tionalradiationmustbeatleast10cerg/cmday.4Thiswouldimplyamasslossfromthecenterofthegalaxyofabout20000Mo/yr.Itisthereforepossiblethatthemassofthegalaxymighthavebeenconsiderablyhigherinthepastthanitisnow.Thismakesitimportanttoestimatetheefficiencywithwhichrest-massenergycanbeconvertedintogravita-tiona
10、lradiation.Clearlynuclearreactionsareinsufficientsincetheyreleaseonlyabout1%oftherestmass.Theefficiencymightbehigherineitherthenonsphericalgravitationalcollapseofastarorthecollisionandcoalescenceoftwocollapsedobjects.Uptonownolimitsontheef-ficiencyoftheprocesseshavebeenknown.TheobjectofthisLetterist
11、oshowthatthereisalimitforthesecondprocess.Forthecaseoftwocollidingcollapsedobjects,eachofmassmandzeroangularmomentum,theamountofener-gythatcanbecarriedawaybygravitationaloranyotherformofradiationislessthan(2-v2)m.Iassumethe validityoftheCarter-Israelcon-jucturethatthemetricoutsideacollapsedob-jectse
12、ttlesdowntothat ofoneoftheKerrfamilyofsolutionswithpositivemassmandangularmomentumaperunitmasslessthanorequaltom.(IamusingunitsinwhichG=c=1.)Eachofthesesolutionscontainsanonsingulareventhori-zon,two-dimensionalsectionsofwhicharetopo-graphicallysphereswitharea8wmm+(ma).-Theeventhorizonistheboundaryof
13、theregionofspace-timefromwhichparticlesorphotonscanescapetoinfinity.Ishallconsideronly1344Vor.vMz26,NvMsER21PHYSICALREVIEWLETTERS24Mar1971space-timeswhichareasymptoticallyflatinthesenseofbeingweaklyasymptoticallysim-ple.ThemetriconsuchaspaceMcanbeex-tendedeonformallytoamanifoldwithboundaryiBwhichcon
14、sistsofMand twonullhypersur-faces&and8.Theserepresentfutureandpastnullinfinity,respectively.TheeventhorizoncanthenbedefinedasJ(8),whereadotindi-catestheboundary,andforanysetI,J(3)isthecausalpastof8,i.e.,thesetofallpointsthat canbereachedfrom3bypast-directednon-spacelikecurves.ThesituationthatIconsid
15、erisoneinwhichthereareinitiallytwocollapsedobjectsorblackholesaconsiderabledistanceapartinasymp-toticallyflatspace.Theblackholesareassumedtohaveformedatsomeearliertimeasaresultofeithergravitationalcollapsesortheamalga-mationofsmallerblackholes.Thissituationcanbedescribedintermsofaspacelikehyper-surf
16、aceZ,.whichisaCauchysurfacefortheasymptoticallyflatregionofspace-time.OnZ,.therewillbetwoseparateregions,B,andBwhichcontainclosed,trappedsurfaces.InfactthesurfaceZ,.neednotexistwithintheregionsB,andB,sincewhathappenstherecannotaffectwhathappensoutside.JustoutsideB,andB,willbetwotwo-sphereswhichareth
17、eintersec-tionofJ(8)withZ,BytheCarter-Israelcon-jecturetheareasofthesetwosphereswillbetoagoodapproximationgivenbyformula(1)forthevaluesma,andma,ofthemassesandspecif-icangularmomentaofthetwoblackholes.Sup-posenowthatthetwoblackholescaptureeachotherto formasingleblackholewhichsettlesdowntoaKerrsolutio
18、nwithparametersm,anda,.Therewillthenbealaterspacelikehypersur-m+m-a&mm+M-a+Bytheconservationlawforasymptoticallyflatspace,4theenergyemittedingravitationalorotherformsofradiationism,+m,-m,.Theeffi-ciencye=(m,+m,)(m,+m,-ms)islimitedbyEq.(2).Thehighestlimitoneis2whichoccursifm,=me=a,=aa,0.Ifa,=a, =0,th
19、ene&(1-2).Itshouldbestressedthattheseareup-perlimits.Theactualefficiencymightbemuchless.Imagineasituationinwhichtherewereinitial-lyalargenumberofblackholes.Firstthesecouldcombineinpairs,andthentheresultingholescouldcombine,andsoon.Ondimensionalgroundsonecouldexpecttheefficiencytobethesameateachstage
20、.Thus onewouldextractafaceZ&onwhichtherewillbeasingleregionB3containingclosedtrappedsurfaces.JustoutsideB,willbeatwo-sphereZAJ(0)whoseareaisgivenbyformula(1)withm,anda,.NowJ(8)isgeneratedbynullgeodesicsegmentswhichmayhavepastendpointsbutmhichcanhavenofutureendpoints.Ishalltakeitthattherearenosingula
21、ritiesintheexteriorregionJ(8)AJ(Z,.).Whethersuchnakedsingulari-tiescanoccurorwhetherthesingularitiesarealwayshiddenbehindtheeventhorizonisanun-resolvedquestion.Onewouldnotexpecttoob-tainalimitontheenergythatcouldbecarriedtoinfinitybygravitationalradiationiftherewereanakedsingularitysincewhathappensa
22、tasin-gularityisnotgovernedbyanyknownlaws.IshallthereforeconsideronlythosesituationswherewhathappensinJ(d)CLJ(Z,.)isdeter-minedbydataonZ,i.e.,whereZ,.isaCauchysurfaceforZ(&)AJ(Z,).OnecanchooseZzsothatitisaCauchysurfaceforZ(s)AJ(Zz)andshowthateverynullgeodesicgeneratingseg-mentofJ(5)inJ(Z,.)AJ(Z&)mus
23、tintersectZz.BytheCarter-Israelconjecturethesolutionin7(8)AJ(Z)resemblestheexteriorKerrsolutionandsocontainsnosingularities.ThuseachnullgeodesicgeneratingsegmentofJ(8)in4(Z)willbegeodesicallycompleteinthefu-turedirection.Iassumealsothattheweakener-gyconditionholds:TKK0foreverynullvectorK.Itthenfollo
24、wsthattheconvergencepofthenullgeodesicgeneratorsofJ(d)cannotbepositiveanywheresinceifitweretherewouldbeacausticandhenceafutureendpointofsomeofthegenerators.ThisshowsthattheareaofZAJ(&)mustbegreaterthanorequaltotheareaofZ,A.J(S)(infact,itmustbestrictlygreater).Therefore,+(2g2)1/2(2)verylargefractiono
25、ftheoriginalmass(thisar-gumentwassuggestedbyC.W.Misner).Ateachstagetheemittedburstswouldbelongerandstronger.Thismightexplain%chersobserva-tions.Onecanalsoapplythisresultthattheareaontheeventhorizonincreasestothecaseofasin-gleblackholeonwhichvariousparticlesandfieldsimpinge.Onethenhasthatthefinalmass
26、mandspecificangularmomentuma,mustsatis-fytheinequalitymm+(m-a)&mm+(m-a)wherem,anda,aretheinitialvalues.Inpartic-VOLUME26,NUMBER21PHYSICA,LREVIEWLETTERS24Mz1971ular,ifa,isequaltozero,then2m,&m,m,+(m,-a,).UsinganideaofPenrose,Chris-todolouhasshownthatonecangetarbitrarilynearthislimit.Onecaninterpretth
27、isasex-tractingtherotationalenergyof theblackhole.J.Weber,Phys.Rev.Lett.22,1320(1969).J.Weber,Phys.Rev.Lett.24,276(1970).J.Weber,Phys.Rev.Lett.25,180(1970).G.W.GibbonsandS.W.Hawking,TheDetectionofShortBurstsofGravitationalRadiation(tobepub-lished).5G.B.Field,M.J.Bees,andD.W.Sciama,Com-mentsAstrophys
28、.SpacePhys.1,187(1969).B.Carter,Phys.Rev.Lett.26,331(1971).W.Israel,Phys.Rev.164,17761967).8R.H.BoyerandR.W.Lindquist,J.Math.Phys.8,265(1967).R.Penrose,privatecommunication.R.Penrose,inBattelleRencontxes2967,editedbyC.M.deWittandJ.A.Wheeler(Benjamin,NewYork,1968).R.PenroseandS.W.Hawking,Proc.RoySoc.
29、Ser.A314,529(1970).S.W.Hawking,Proc.Roy.Soc.,Ser.A300,187(1967).R.Penrose,Riv.NuovoCimento1,Num.spec.,252(1969).H.Bondi,M.G.J.vanderBurg,andA.W.K.Metz-uer,Proc.Roy.Soc.,Ser.A269,21(1962).R.Penrose,Phys.Rev.Lett.10,66(1963).D.Christodolou,Phys.Rev.Lett.25,1596(1970).HeavyMesonsandNeutralAxial-VectorC
30、urrents*P.CarruthersLaboratoryofNuclearStudies,CornellUniversity,Ithaca,NewYorh14850(Received1April1971)Itissuggestedthattheeighthandninthaxial-vectorcurrentsaredominatedbytheJ+=0mesousq(549),q(958),audthe(presumed)J=1+mesonsD(1285)audE(1242).Pre-dictionsaremadeconcerningthedecaymodesofDand8aswellas
31、fortheDNAandENNcouplings.Theexistenceofanoctetofaxial-vectorcur-rentsmayberegardedaswellestablished.How-everthestatusofapossibleninthcurrentFo,anaxialbaryoncurrent,hasremainedobscure,withsomeauthorsdoubtingitsexistenceandoth-ersascribingspecialvirtuestoit.Inthepresentnotewesuggestthattheg(960)andE(1
32、422)aremanifestationsofthiscurrentandsuggestexper-imentalmeansofilluminatingthisquestion.Atthesametimewepresentaparallelinterpreta-tionoftheeighthaxialcurrent5,intermsofthepropertiesoftheq(550)andD(1285)mesons,ThedecaymodesofDandEarerathersimi-lar,withrprmandKKmwithKKcomingfromthe0statem(1016)observ
33、edforbothmesons.(TheEmesonalsodecaysthroughKK*,whichiskinematicallyforbiddenforD.)ApartfromtheK*I7mode,weinterpretthegemandEZmfinalstatesasduetothesequenceD(E)-egorD(E)-7lwithsubsequentdecays-27t,m-vtq,andv-KZ.Asinanearlierpaperweconsidereand7Ttobemembersofascalarnonet.Inthefollowingmeshallrelatethe
34、axial-scalar-pseu-doscalarcouplingstothescalar-pseudoscalar-pseudoscalarcouplingsbyauniversalityargu-mentbasedonpartialconservationofaxial-vec-torcurrent(PCAC)forallnineaxial-vectorcur-rents.Weconsiderthenineaxial-vectorcurrents$+(i=0,8).ThematrixelementsoftheisospincurrentFmayberegardedasdominatedb
35、ythen(0)andtheA,(1).Sincethereisa.nonetofpseudoscalarstheninthbeingq(958),itisrea-sonabletoaskaboutacompanionnonetofaxial-vectormesonsandfurthertospeculatethatthe(0,1)nonetsdominatethecorrespondingcur-rents.Theexperimentalsituationisunclear,butitappearsthattheA,(1070), D(1285),K(1240),andE(1422)areg
36、oodcandidatesforanonet.ComparisonwiththepseudoscalaroctetsuggeststhatDismostlyoctetandEthesinglet.WiththisassignmenttheassumedA,andKmassesimplythatthemixingisnegligible.Sinceqgmixingissmall(sl0),weshallignoremixinghereandassociatethepairs(q,D)and(g,E)withtheunmixedcurrents5,and7,&,respec-tively.Thecouplingconstantsg,D,g,D,etc.,mayberelatedtog,gbyageneralizationofauniversalityargumentproposedinRef.3forthe(n,A,)complex.Thematrixelement(vFe)isgivenintermsoftheformfactorsF,andF,