Phase transition in modified thermodynamics of Kerr-AdS black holes

In this study,we investigate the critical phenomena of Kerr-Ad S black holes under the modified first law of thermodynamics.Specifically,we considered modified black hole thermodynamics that exhibit a van der Waalslike phase structure.All critical exponents were calculated,and then,a swallowtail diagram of free energy was plotted.Comparing with existing results,the main difference is the correspondence between the thermal quantities of Kerr-Ad S 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（?H,J）→（V,P）,while in our study,the correspondence was（J,■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（■H,J） cross-section,causing the difference in correspondence.