Abstract
In this study,we investigate the critical phenomena of Kerr-AdS black holes under the modified first law of thermodynamics.Specifically,we considered modified black hole thermodynamics that exhibit a van der Waals-like phase structure.All critical exponents were calculated,and then,a swallowtail diagram of free energy was plot-ted.Comparing with existing results,the main difference is the correspondence between the thermal quantities of Kerr-AdS black holes and the van der Waals system.In a previous study[Y.D.Tsai,X.N.Wu,and Y.Yang,Phys.Rev.D 85 044005(2012)],the correspondence was(ΩH,J)→(V,P),while in our study,the correspondence was(J,(Ω)H)→(V,P).This difference was owing to the rotating effect.The modified black hole thermodynamics were associated with rotating observers.The free energy in such a reference contains extra rotating energy,which induces a Legendre transformation in the((Ω)H,J)cross-section,causing the difference in correspondence.
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