Lapiedra Departament dAstronomia i Astrof305sica Universitat de Valencia With Juan M Aguirregabiria and J A MoralesLladosa brPage 2br 1INTRODUCTION After selecting a suitable energymomentum complex one can derive some expression for the linear and ID: 72179
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1.-INTRODUCTION Afterselectingasuitableenergy-momentumcomplex,onecanderivesomeexpressionforthelinear,P ,andangularJ ,4-momentaforagivenspace-timeinGeneralRelativity, ;;:::=0;1;2;3:-S.Weinberg,GravitationandCosmology(JohnWileyandSons,1972) WeselecttheWeinbergcomplexbyreasonsexplainedin-R.LapiedraandJ.A.Morales,Gen.Relativ.Gravit.(2013)451145 These4-momentaaredramaticallydependentonthecoordinatesused. Then,wedeneintrinsicP andJ valuesastheonescalculatedinintrinsiccoordinates-R.LapiedraandJ.A.Morales,Gen.Relativ.Gravit.(2013)451145StabilityofcreativenessofSchwarzschildmetricERE-2013,Benasque2 2.-CREATABLEUNIVERSES PeoplehavespeculatedaboutthepossibilitythatourUniversecomefromavacuumquantum uctuation.-M.G.Albrow,Nature241(1973)56;E.P.Tryon,Nature246(1973)396 Theideahasbeendevelopedlately-A.Vilenkin,Phys.Rev.D32(1985)2511 Wecouldthenconjecturethatthecorrespondingspace-timeshouldhavevanishingintrinsic4-momenta. Wehavecalledclassicallyself-creatable(creatableforshort)thespace-timeswithvanishing4-momentaP =0;J =0;Jijcomponentsvanishingirrespectiveofitsorigin.-R.LapiedraandJ.A.Morales,Gen.Relativ.Gravit.(2012)44367StabilityofcreativenessofSchwarzschildmetricERE-2013,Benasque4 4.-THEADMENERGYEXPRESSION Foraregularenoughspace-time,wecanwritetheenergyP0derivedfromtheWeinbergcomplexastheADMenergy,i.e.,thefollowing2-surfaceintegralP0=1 16Z(@jgij�@ig)d2i-R.Arnowitt,S.DeserandC.W.Misner,inGravitation:anintroductiontocurrentresearch(JohnWiley,1962).GravitationalconstantG=speedoflightc=1,gij:3-spacemetriccomponentsi;j;:::=1;2;3;repeatedindicesaresummed,gijgij,ijistheKroneckersymbol,2istheboundaryofthe3-space,d2iisthe2-surfaceelementofintegration.StabilityofcreativenessofSchwarzschildmetricERE-2013,Benasque6 6.-ISTHECREATIVENESSOFTHESCHWARZSCHILDMETRICSTABLE? IsthiscreatablecharacteramereartifactoftheextremesymmetryoftheSmetricdeprivedofanyphysicalmeaning? Totestthis:weconferaslowrotationtoournonrotatingstar. Thatis,weconsiderthecorrespondingLense-ThirringmetricKerrmetric,linea-rizedintheaparameter(theangularmomentumperunitmass),farawayenoughfromthecenter. Inagivenfamilyofintrinsiccoordinates,(T;;;),thislinearizedmetriccanbewrittenasds2=�dT2+ rd2+r2(d2+sin2d2)�2ap r0 r[1+r3h0(R)]sin2ddwith= +a r0h2r r r0+lnp r�p r0 p r+p r0i+ar0h(R);handarbitraryfunction,R2 3p r0(3=2+C),andh0dh=dR.StabilityofcreativenessofSchwarzschildmetricERE-2013,Benasque8 8.-FUTUREWORK:ADDRESSINGTHEQUANTUMCREATIONQUESTION InordertoestimatetheprobabilityofcreationofaSchwarzschildmetric,inourGausscoordinates,throughquantumtunnelling(seeforexampleA.Vilenkin,PRD32,2511(1985)),welookforwardtocalculatetheactionvalueofthecorrespondinginstanton.Acknowledgments:ThisworkwassupportedbytheSpanish\MinisteriodeCienciaeInnovacion",projectFIS2010-15492andBasqueGovernment,projectIT592-13(J.M.Aguirregabiria)andbytheSpanish\MinisteriodeEconomayCompetitividad",MICINN-FEDERprojectFIS2012-33582(R.LapiedraandJ.A.Morales-Lladosa).StabilityofcreativenessofSchwarzschildmetricERE-2013,Benasque10