Hawking-1966-PhD 霍金博士论文

Lr1;.i.,··r~...,tor:::::.RI)I...;r:\,~·.FOR·.:Ph.D•'l...,0-----(JJ.',-----f\JIV•ilJlit\C.AMllrdc,Ef'i;rn~EARUJSTUDIE.S.,-,f.'-:i;~~.r.,·r~'.·..__.'•.,.,:,.~~.,tFEB1966r,t·,Jn.r'o,-·ofh.1..t._,;.w,ome1.1.1l:ial;i011s,.m1Jcon;ou0nC'Gofth.cx,)tU:-;:io,or-,1:cniv(i1:..,c.Ln;.H....pte-,_,·ii.;.LsGhont;1·tcl.,ex1...i11CI:ae..,·L'.r0liffic1.lticuf'oJ:l;hn1oy.e-.,··VJ.vuion.,.1apLe.r'oaLJ.d.tu.pc·l.;u_·b...d,ion.,o.C...,n:,:..n.i.11._,101,10o:ou:,;:..Yltisocro)'tvunivoi':_,•h:c.:o1~Lu,.Jion;'.cc..,ulLo'th·J.'O,!..il...I.,·.1.·_.i.;:..;(!)0:;.i..u.d),.,tiorl;,Ll1t;rot.ii-iVi.'.J.Ily•-'I......1'·.J.'ho;ro)·,i,ion,dub~;i.',t1onoi'rvi-l,t;lonul1:ui..tioL,·~L.,oi1vc:.,tl1,cinti..;i11·0'{·mu.ti·vil;:Lion1r:ttl.ti0i..,ox·.1in,,'~.,L10aod:..,.,1...)otic..:1•un..;ic.m_;.•hI•)t'.Lin4•.,·)en.v.i.our::..rl.Li1:·n.;1,toVc·'ll)c..tC'C('J'iV.d..)h')t(HL,..~1,wit_i;ltoi:.;u·1:011c,,o.',_,·nulJLi3inCOJMoloJCloGl.J.__ti..,shomtll,t...:lul.·r:it;,.,i'1.it)1n()('()ViC(t0i0l.v·t0t}'Il•0V()!.'VOi0J.I.•·r,,'Vli•,]'VllC...lV;iT0...lv0(•t'io·,1;..c.l.0iV•00,.,u(;.C'0lr.k~o..lli,iVI.,'0•)\I..[)·1il1.,.--,t0(lo-•.io·(Ii•;o'',...I.,i..,tothanly....u_)orviso..:·,1Jr.)•.•clc..!llf1.1_....,hcl1),.n:.....d.vicodur·in.~.yp0rioofr.rnoorc,1.tould.....loolil::ctothanlrr.}.:.·tert.ndlh.G..t.1•,1;11.is1or.,,1yuc...i'uldiGuuu..,io_na.I;_.Lndeb·Lec1oH.G•.c.Lon:.i1:.nl'orthocn.lcllll,tionofl,llo'ioncli.ldcntii;iosinvi'pto.rj.horenor.rchCLC,jcribedi11GhiLt1esis~,.GJJ.u.l..l.•:.;,tllOclioJOI'9'.)i.•.Haul~in'IQ1.IntroductionCHAPTER1TheHoyle-NarlikarTheoryofGravitationThesuccessofMaxwell'sequationshasledtoelectrodynamicsbeingnormallyformulatedintermsoffieldsthathavedegreesoff!eedomindependentoftheparticlesinthem.However,Gausssuggestedthatanaction-at-a-distancetheoryinwhichtheactiontravelledatafinitevelocitymightbepossible.Thisideawasdevelopedby~heelerandFeynman(4,2)whoderivedtheirtheoryfromanaction-principlethatinvolvedonlydirectinteractionsbetweenpairsofpart­icles.Afeatureofthistheorywasthatthe'pseudo'-fieldsintroducedarethehalf-retardedplushalf-advancedfieldsclaculatedfrom~heworld-linesoftheparticles.However,W1eelerandFeynman,and,inadifferentway,Hogatth(3)wereabletoshowthat,providedcertaincosmologicalconditionsweresatisfied,thesefieldscouldcombineto~ivetheobservedfield.HoyleandNarlikar(4)extendedthett1eorytogeneralspace-timesandobtainedsimilartheoriesfortheir'C'-field(5)andforthegravitationalf~eld(G).Itiswiththesetheoriesthatthischapterisconcerned.....•...•...IItwillbe:3hownthatinanexp,..ndinguniversetheadvancedfieldsareinfinite,andtheretardedfieldsfinite.~hisisbecause,unlikeelectriccharges,allnJasseshHVAthe2.TheBoundaryConditionHoyleandNarlikarderivetheirtheoryfromtheaction:wheretheintegrationisovertheworld-linesofparticles0.b.....IInthisexpression(isaGreenfunction.thatsatisfiesthewaveequation:wherejisthedeterminantof3.j.3incethedoubleintheactionAissymmetricalbetweenallpairsofparticlesG..)b,onlyth&.tpartofc;-(o...b)thatissumsyrmnetricalbetweencandbwillcontributetotheactioni.e.theactioncanbewrittenA::where~-.Ar(C\,b)='.I'hus(itmustbethetime-symmetricGreenfunction,bewritten:q~=fqre-t,..jqo..dvwhereandcanandCic,._Jvaretheretardedc:.ndadvancedGreenfunctions.u~reouirin~thattheactionbestationarvundervariations,I.JJ--Jofthe3~HoyleandNarlikarobtainthefield-equations:[£.Z.~{Vl,(o.){X)/Vl(b)(x)](lik-±scKR)C\..-fb.:I(a.);r-(b)J-7:QLKfVLtv\J:ri,,.mereconsequenceoftheparticularchoiceofGreenfunction,thecontractionofthefield-equationsissatisfiedidenticall:!.~herea~ethusonly9equationsforthe10componentsofQ··'._JVJandthesystemisindeterminate.[c..)HoyleandNarlikarthereforeimposef.m=fYl0=const.,-tlsthetenthequation.Bythenmakin~the'smboth-fluid'..L~11A(o.),1;,{b)r-,/\rt2approximation,thatisbyputtingL~1•v··~--,,~Q.:/b-.-(J)theyobtaintheEinsteinfield-equations:..!....V\..~{R.-.!_R_')~fO..I:2.5V-:-f,.KThereisanimportantdifference,however,betweenthesefield-equationsinthedir~ct-particleinteractiontceoryandintheusualgeneraltheoryofrelativity.Inthegeneraltheoryofrelativity,anymetric~hatsatisfiesthethefield-equationsisadmissible,butinthedirect-particlainteractiontheoryonlythosesolutionsofthefield-equationsareadmissiblethatsatisfytheadditionalrequirement:/VL,C)(X.)-::.£)C/:,:,°')claii£rC;;(-:r:.)°')clo--J0..V.Thisrequirementishighlyrestrictive;itwillbeshownthatitisnotsatisfiedforthecosmologicalsolutionsofthe~insteinfield-equations,anditappearsthatitctnnotbesatisfiedforanymod.elso.ftheuniver;:;etho.teithercontainaninfiniteamountofmattero~undergoinfiniteexpansion.ThedifficultyissimilartothatoccurringinNewtoniant~corywhenitisrecognizedthattheuniversemightbeinfinite.TheNewtonianpotentialtobeystheequation:1.r.Jherelisthedensity.Inaninfinitestaticuniverse,fwouldbeinfinite,sincethesourcealwayshasthesameGign.Thedifficultywasresol­vedwhenitwasrealizedth~~ttheunivers8wasexpand.ins,.sinceinanex-oanclinguniversetheretardedsolutionoftheaboveequationisfinitebyasortof'red-shift'effect.Theadvancedsolutionwillbeinfinitebya'blue-shift'effect.fhisisunimportantinNewtonianthe6ry,sinceoneisfreetoc