A gravitational theoretical development supporting MOND

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1、AgravitationaltheoreticaldevelopmentsupportingMONDEdmundA.Chadwick,TimothyF.HodgkinsonandGrahamS.McDonaldSchoolofComputing,ScienceandEngineering,UniversityofSalfordSalfordM54WT,UKE.A.C.andT.F.H.contributedequallytotheformulation,analysesandinterpretation.Theauthorsarethuslistedinalphabeticorder.G.S

2、.M.’scontributionwashelpwiththepoint-sourcesolutions.AbstractConformalgeometryisconsideredwithinageneralrelativisticframework.Anin-variantdistantforpropertimeisdefinedandaparalleldisplacementisappliedinthedistortedspace-time,modifyingEinstein’sequationappropriately.Aparticularsolutionisintroducedfor

3、thecovariantaccelerationpotentialthatmatchestheobservedvelocitydistributionatlargedistancesfromthegalacticcentre,i.e.ModifiedNewtonianDynam-ics(MOND).Thisexplicitsolution,ofageneralframeworkthatallowsbothcurvatureandexplicitlocalexpansionofspace-time,thusreproducestheobservedflatteningofgalaxys’rotat

4、ioncurveswithouttheneedtoassumetheexistenceofdarkmatter.Thelargedistanceexpansionrateisfoundtomatchthespeedofasphericalshockwave.1IntroductionThemotionofstarsaroundspiralgalaxiestraceflatrotationcurveswhichdonotequatetothosecalculatedfromNewtoniandynamicsappliedtotheluminousmatterofthegalaxy[1].Onep

5、ossibleexplanationforthisistheexistenceofnon-luminousdarkmattersuchasWeaklyInteractingMassiveParticles[2]which,whenincludedinthecalculation,reproducearXiv:1307.3937v1[gr-qc]15Jul2013theobservedvelocityprofiles.Observationsmadeonthebulletclusterofgalaxiessuggesttheexistenceofdarkmatter[3],althoughoth

6、ereffectshavealsobeenattributedtotheseobservations[4].Anotherpossibleexplanationisthatgalacticmotionsaregovernedbynon-Newtonianphysics.ThisviewpointisbackedbytheTully-Fisherrelation[5]thatshowsacorrelationbetweenthespeedofrotationofstarsandluminosityinagalaxywithouttherequirementfordarkmatter.Onesug

7、gestionisamodificationtoNewtoniandynamicsnamedMOND[6]whichproducesthemotionsofspiralgalaxies,andMcGaugh[7]hasdemonstratedthatitalsofitsthemotionsforgas-richgalaxies.ArelativisticgravitationtheorytosupportMOND