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1、MimickBlackHole--ReadingnoteforintroductiontoquantumfieldtheoryGuangjieLi14344013DepartmentofPhysics,SchoolofPhysicsandYat-SenSchool,SunYat-SenUniversitySeptember4,2016IntroductionGeneralrelativitypredictslotsoffascinatingphenomenon.Butthesepredictionsarereallydifficulttofind.Recently,the
2、gravitationalwaveisconfirmedbyLIGOafteracentury.Forthedifficultytofindarealblackhole,somephysicisttriedtomimickablackholeinlaboratory.Therearetwomainmethodstoachievethisidea.Wecanchangetheindexofrefraction?,generallyspeaking,it's?and?indielectric,whichresultsfromthesimilarityofMaxwellequa
3、tionsingravitationalfieldandindielectric.Also,youcancontrolairrotationalfluidtomimickamasslessscalarfield.Theequationofmotionforfluidcanbelinearizedtoaformlikeamasslessscalarfieldinacurvedgeometry.1Gravitationallensing[1]‘’Duringthetotalsolareclipsein1919,ArthurEddingtonandcollaboratorspe
4、rformedthefirstdirectobservationoflightdeflectionfromtheSun,therebyvalidatingEinstein’stheoryofgeneralrelativity.AccordingtoEinstein’stheory,thepresenceofmatterenergyresultsincurvedspacetimeandthecomplexmotionofmatterandlightalonggeodesictrajectoriesthatarenolongerstraightlines.Thegeneral
5、theoryofrelativityhasbeenhighlysuccessful,withmanyofitspredictionsvalidated,includingtheprecessionofMercury,gravitationaltimedilationandgravitationalredshift,expansionoftheuniverseandframe-dragging.GiventheanalogybetweenthemacroscopicMaxwell’sequationsincomplexinhomogeneousmediaandfree-sp
6、aceMaxwell’sequationsforthebackgroundofanarbitraryspacetimemetric.’’Ingravitationalfield,Maxwellequationsare:?⋅?=4???⋅?=01??×?=−(√??)?√???1?4??×?=(√??)+??√????Where,γisthedeterminantof???=−g??+ℎg?g?.Forastaticgravitationalfield,?⋅?=4???⋅?=01???×?=−???1??4??×?=+?????WhichisexactlytheMaxwel
7、lequationsinmedia.Theonlydifferenceistherelationbetween?and?,?and?.And,itgivesanalogybetweentheMaxwellequationsingravitationalfieldandindexofrefraction-varyingmedia.1?=?=√g001.1Spacetimeandpressure-densityrelationConsideracentrally-symmetricisotropicSchwarzchild-lik
