Entropy Corrected Thermodynamic Geometries of Regular Black Holes

Abstract

In thisthesis,weexplorethethermodynamiccharacteristicsofaBardeen blackholethatinteractswithastringcloudandisminimallyconnectedto nonlinear electrodynamics.Wepresentaentropyfunctionwith¯veparame- ters, demonstratingitssingularity-freebehaviorthroughouttheentirecos- mic evolutionoftheuniverse.Moreover,thisfunctionservestoextendthe Tsallis, R¶enyi,andSharma-Mittalentropiesforappropriateparameterlimit conditions.ForinstancetheTsallisentropyisexpressedas ST = S±, where ± representstheTsallisexponentand S denotes theBekenstein-Hawking entropy.Thisformulaisparticularlyapplicabletosystemswithlong-range interactionswheretheBoltzmann-Gibbsentropyisnotsuitable.It'sevident that when ± = 1,theTsallisentropyconvergestotheBekensteinHawking limit, butforvaluesof ± other than1,itdoesnotexhibitadditivity.On the contrary,theR¶enyientropyitconvergestotheBekenstein-Hawking limit asaapproacheszero.WhiletheTsallisandR¶enyientropiesmightbe combinedtogeneratetheSharma-Mittalentropy,theR¶enyientropywas ¯rst o®eredasawaytoassessinformationcontent.Weanalyzeavariety of parameters,includingmass,temperature,pressure,andGibbsfreeen- ergy,usingtheTsallis,R¶enyi,andSharma-Mittalentropies.Inourstudy, wederivestablebehaviorand¯ndphysicalsolutionsbytakingparticular valuesfortheparameters a and q.