Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space (2308.00489v1)

Abstract: We analyse the restricted phase space thermodynamics (RPST) of Kerr-Sen-AdS black holes with the central charge $C$ and its conjugate chemical potential $\mu$ but exclude the familiar $PdV$ term in the first law of black hole thermodynamics. That gives rise to a new perspective on the thermodynamics of black holes. Using the scaling properties, we investigate the first law and the corresponding Euler formula. Such formalism has its beauty, to say, for example, the mass is considered to be a homogeneous function of the extensive variables in the first order. In contrast, the intensive variables are of zeroth order. Because of the complicated expressions of the metric, we numerically calculate the critical values of the thermodynamic quantities. We find the phase transition behaviour of the free energy and other thermodynamic conjugate variables that appear in the first law. The RPST of the Kerr-Sen-AdS black holes is like that of the Reissner-Nordstr$\ddot{o}$m-AdS and the Kerr-AdS black holes. Such notions of the phase transition behaviour show that there should be some underlying universality in the RPST formalism.