We consider a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically light-like branes for any odd world-volume dimension, hence the acronym WILL-branes (Weyl-Invariant Light-Like branes). We discuss in some detail the prop

Whenputinagravitationalblackholebackground,theWILL-membrane(p=2)sitson(“ma-terializes”)theeventhorizon.

Whenmovinginbackgroundproduct-spaces(“Kaluza-Klein”context)theWILL-membranede-scribesmasslessmodes,eventhoughthemembraneiswrappingtheextradimensionsandthere-foreaquiringnon-trivialKaluza-Kleincharges.

ThecoupledEinstein-Maxwell-WILL-membranesystem(52)possessesself-consistentsolutionwheretheWILL-membraneservesasamaterialandelectricallychargedsourceforgravityandelectromagnetism,andit“sits”on(materializes)thecommoneventhorizonforaSchwarzschild(intheinterior)andReissner-Nordstr¨om(intheexterior)blackholes.Thusourmodel(52)providesanexplicitdynamicalrealizationofthesocalled“membraneparadigm”inthephysicsofblackholes[13].

TheWILL-branescouldbegoodrepresentationsforthestring-likeobjectsintroducedby’tHooftinref.[14]todescribegravitationalinteractionsassociatedwithblackholeformationandevapo-ration,sinceasshownabovetheWILL-braneslocatethemselvesautomaticallyinthehorizonsand,therefore,theycouldrepresentdegreesoffreedomassociatedparticularlywithhorizons.ThenovelclassofWeyl-conformalinvariantp-branesdiscussedabovesuggestsvariousphysicallyinterestingdirectionsforfurtherstudy:quantization(Weyl-conformalanomalyandcriticaldimen-sions);supersymmetricgeneralization;possiblerelevancefortheopenstringdynamics(similartotheroleplayedbyDirichlet-(Dp-)branes);WILL-branedynamicsinmorecomplicatedgravitationalblackholebackgrounds(e.g.,Kerr-Newman).

Acknowledgements.Twoofus(E.G.andE.N.)aresincerelygratefultoPlamenFizievandtheorganizersoftheSecondWorkshoponGravity,AstrophysicsandStringsforthekindinvitationtopresenttheretheaboveresults.E.N.andS.P.arealsothankfulforhospitalityandsupporttotheorganizersofthe2ndAnnualMeetingoftheEuropeanRTNEUCLID,Sozopol(Bulgaria),2004.Oneofus(E.G.)thankstheInstituteforNuclearResearchandNuclearEnergy(So a)andTriesteUniversityforhospitality.HealsoacknowledgesusefulconversationswithGerard‘tHooft,EuroSpallucciandStefanoAnsoldi.

E.N.andS.P.arepartiallysupportedbyBulgarianNSFgrantsF-904/99andF-1412/04.Finally,allofusacknowledgesupportofourcollaborationthroughtheexchangeagreementbetweentheBen-GurionUnivesityoftheNegev(Beer-Sheva,Israel)andtheBulgarianAcademyofSciences.

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