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Softhairsonisolatedhorizonimplantedbyelectromagneticfields InspiredbytherecentproposalofsofthaironblackholesinHawkingetal(2016Phys.Rev.Lett.116231301),wehaveshownthatanisolatedhorizoncarriessofthairsimplantedbyelectromagneticfields.ThesolutionspaceandtheasymptoticsymmetriesofEinstein–Maxwelltheoryhavebeenworkedoutexplicitlyneartheisolatedhorizon.TheconservedcurrenthasbeencomputedandaninfinitenumberofnearhorizonchargeshavebeenintroducedfromtheelectromagneticfieldsassociatedwiththeasymptoticU(1)symmetrynearthehorizon,whichindicatesthefactthattheisolatedhorizoncarriesalargeamountofsoftelectrichairs.Thesoftelectrichairs,i.e.asymptoticU(1)charges,areshowntobeequivalenttotheelectricmultipolemomentsofisolatedhorizons.Itisfurtherarguedthattheisolatedhorizonsupertranslationisfromtheambiguityofitsfoliationandananalogueofmemoryeffectonhorizoncanbeexpected. FromPrigoginetoRaychaudhuri ItishighlightedbyPrigoginethattherearetwoadditionaluniversalbehaviorsassociatedwiththeentropyproductionratebesidesthefourlawsofthermodynamics.Oneisthattheentropyproductionratedecreaseswhenthesystemapproachesthesteadystate,andtheotheristhattheentropyproductionratereachesitsminimalvalueatthesteadystate.MotivatedbytheblackholethermodynamicsandAdS/CFTcorrespondence,weresorttotheRaychaudhuriequationtoprovethatthesetwouniversalbehaviorsarealsoobeyedbytheblackholeentropy.Inparticular,ourresulttogetherwiththefourlawsofblackholethermodynamicsfurtherindicatesthattheholographicgravityshouldbeuniversal,notrestrictedonlywithinthecontextofAdS/CFTcorrespondence. Holographicinterpretationofacousticblackholes Withtheattempttofindtheholographicdescriptionoftheusualacousticblackholesinfluid,weconstructanacousticblackholeformedinthed-dimensionalfluidlocatedatthetimelikecutoffsurfaceofaneutralblackbraneinasymptoticallyAdSd+1spacetime. Fluid/gravitycorrespondenceforgeneralnon-rotatingblackholes Inthispaper,weinvestigatethefluid/gravitycorrespondenceinspacetimewithgeneralnon-rotatingweaklyisolatedhorizon.WiththehelpofaPetrov-likeboundaryconditionandlargemeancurvaturelimit,weshowthatthedualhydrodynamicalsystemisdescribedbyageneralizedforcedincompressibleNavier–Stokesequation.Specially,forstationaryblackholesorthosespacetimewithsomeasymptoticallystationaryconditions,suchasystemreducestoastandardforcedNavier–Stokessystem. Poorman'sholography:howfarcanitgo? Almostacenturyago,Einstein,afterNewton,shednewlightongravitybyclaimingthatgravityisgeometry.Therehasbeennodeeperinsightbeyondthatlateronexcepttherecentsuspicionthatgravitymayalsobeholographic,dualtosomesortofquantumfieldtheorylivingontheboundarywithonelessdimension.Suchasuspicionhasbeensupportedmainlybyavarietyofspecificexamplesfromstringtheory.Thispaperisintendedtopurporttheholographicgravityfromadifferentperspective.Namely,weshallshowthatsuchaholographycanactuallybeobservedbyworkingmerelywithinthecontextofEinstein'sgravitythroughpromotingBrown–York'sformalism,whereneitheristhespacetimerequiredtobeasymptoticallyAdSnortheboundarytobelocatedatconformalinfinity,whichalsoconformstothespiritinheritedfromWilson'seffectivefieldtheory.Inparticular,weshowthatourholographyworksremarkablywellatleastatthelevelofthermodynamicsandhydrodynamics,whereaperfectmatchingbetweenthebulkgravityandboundaryfluidisfoundforentropyanditsproductionbytheconservedcurrentmethod. GeometrieswiththeSecondPoincaréSymmetry ThesecondPoincarékinematicalgroupservesasoneofnewonesinadditiontotheknownpossiblekinematics.ThegeometrieswiththesecondPoincarésymmetryispresentedandtheirpropertiesareanalyzed.Onthegeometries,thenewmechanicsbasedontheprincipleofrelativitywithtwouniversalconstants(c,l)canbeestablished. IncompressibleNavier–StokesequationfromEinstein–MaxwellandGauss–Bonnet–Maxwelltheories Thedualfluiddescriptionforageneralcutoffsurfaceatradiusr=rcoutsidethehorizoninthechargedAdSblackbranebulkspace–timeisinvestigated,firstintheEinstein–Maxwelltheory.Underthenon-relativisticlong-wavelengthexpansionwithparameterϵ,thecoupledEinstein–MaxwellequationsaresolveduptoO(ϵ2).TheincompressibleNavier–Stokesequationwithexternalforcedensityisobtainedastheconstraintequationatthecutoffsurface.Fornon-extremalblackbrane,theviscosityofthedualfluidisdeterminedbytheregularityofthemetricfluctuationatthehorizon,whoseratiotoentropydensityη/sisindependentofboththecutoffrcandtheblackbranecharge.Then,weextendourdiscussiontotheGauss–Bonnet–Maxwellcase,wheretheincompressibleNavier–Stokesequationwithexternalforcedensityisalsoobtainedatageneralcutoffsurface.Inthiscase,itturnsoutthattheratioη/sisindependentofthecutoffrcbutdependentonthechargedensityoftheblackbrane. FromPetrov-EinsteintoNavier–Stokesinspatiallycurvedspacetime WegeneralizetheframeworkinarXiv:1104.5502tothecasethatanembeddingmayhaveanon-vanishingintrinsiccurvature.DirectlyemployingtheBrown-Yorkstresstensorasthefundamentalvariables,westudytheeffectoffiniteperturbationsoftheextrinsiccurvaturewhilekeepingtheintrinsicmetricfixed.WeshowthatimposingaPetrovtypeIconditiononthehypersurfacegeometrymayreducetotheincompressibleNavier–Stokesequationforafluidmovinginspatiallycurvedspacetimeinthenear-horizonlimit. Newman-Penroseconstantsofstationaryelectrovacuumspace-times AtheoremrelatedtotheNewman-Penroseconstantsisproven.ThetheoremstatesthatalltheNewman-Penroseconstantsofasymptoticallyflat,stationary,asymptoticallyalgebraicallyspecialelectrovacuumspace-timesarezero.StraightforwardapplicationofthistheoremshowsthatalltheNewman-PenroseconstantsoftheKerr-Newmanspace-timemustvanish. UniquenessofKerrspace-timenearnullinfinity WereexpresstheKerrmetricinstandardBondi-Sachscoordinatesnearnullinfinity GRAVITATIONALANOMALYANDHAWKINGRADIATIONOFBRANEWORLDBLACKHOLES Wilczekandhiscollaborators'anomalycancellationapproachisappliedtothe3DSchwarzschild-andBTZ-likebraneworldblackholesinducedbythegeneralizedmetricsintheRandall–Sundrumscenario.Basedonthefactthatthehorizonofbraneworldblackholewillextendintothebulkspacetime,calculationisdonefromthebulkgeneralizedmetricssideanditisshownthatthisapproachalsoreproducesthecorrectHawkingradiationforthesebraneworldblackholes.Besides,sincethisapproachdoesnotinvolvethedynamicalequation,itisalsoshownthattheHawkingradiationisonlyakinematiceffect. Proofoftheentropyboundondynamicalhorizons Theentropyboundconjectureconcerningblackholedynamicalhorizonsisproved.Theconjecturestates,ifadynamicalhorizon,DH,isboundedbytwosurfaceswithareasofABandAB'(AB'>AB),thentheentropy,SD,thatcrossesDHmustsatisfySD≤¼(AB'−AB).WeshowthatthisconjectureisimpliedbythegeneralizedBoussobound.Consequently,thegeneralizedsecondlawholdsfordynamicalhorizons.Finally,weshowthatthelightlikeBoussoboundanditsspacelikecounterpartcanbeunifiedasonebound. OnNewman–Penroseconstantsofstationaryspacetimes Weconsiderthegeneralasymptoticexpressionofstationaryspacetime.UsingtheKillingequation,wereducethedynamicalfreedomoftheEinsteinequationtothein-goinggravitationalwaveΨ0.Thegeneralformofthisfunctioncanbeobtained.Withthehelpofanasymptoticallyalgebraicspecialcondition,weprovethatallNewman–Penroseconstantsvanish. Quasilocalenergy-momentumandenergyfluxatnullinfinity Thenullinfinitylimitofthegravitationalenergy-momentumandenergyfluxdeterminedbythecovariantHamiltonianquasilocalexpressionsisevaluatedusingtheNewman-Penrosespincoefficients.Thereferencecontributionisconsideredbythreedifferentembeddingapproaches.AllofthemgivetheexpectedBondienergyandenergyflux Diffeomorphisminvarianceandblackholeentropy TheNoether-chargeandtheHamiltonianrealizationsforthediff(M)algebraindiffeomorphism-invariantgravitationaltheorieswithoutacosmologicalconstantinanydimensionarestudiedinacovariantformalism.