Preliminary analyses of the dynamics and thermodynamics of rotating regular black holes

We investigate the dynamic and thermodynamic laws governing rotating regular black holes. By analyzing dynamic properties, i.e., the interaction between scalar particles and rotating regular black holes, we establish the criteria that determine whether such black holes satisfy the laws of thermodynamics. In addition, we provide the general form of conserved quantities related to rotating regular black holes, including the relevant flows associated with neutral scalar particles. Meanwhile, we reexamine the relationship between the third law of thermodynamics and weak cosmic censorship conjecture for rotating regular black holes. Based on the abovementioned criteria, we discuss the laws of thermodynamics for three models of rotating regular black holes: Rotating Hayward black holes, Kerr black-bounce solutions, and loop quantum gravity black holes. Our findings indicate that none of the three models satisfies the first law of thermodynamics. In particular, the first and third models fail to comply with the three laws of thermodynamics, whereas the second model satisfies only the second and third laws of thermodynamics. Finally, we attempt to rescue the laws of thermodynamics by modifying entropy or extending the phase space. However, the two scenarios cannot ensure the three laws of thermodynamics in the three models, which reveals an unusual property of rotating regular black holes.