The Critical Phenomena Of Thermodynamics In The AdS Black Hole Background

Thermodynamics of black hole has been one of attractive subjects for many years. Since Hawking radiation was discovered and thermodynamic laws of black hole were bulit in1970s, a great progress has been made in the research on thermo-dynamics of black hole. In this thesis, we make a comparison between eqauations of state in the Van der Waals model and in the Anti-de Sitter (AdS) black hole. And then, we study the critical behavior of AdS black hole in the f(R) theory, such as, phase transition and critical exponents.In chapter1, we present a brief introduction on the development of the theory and thermodynamics of black holes. Firstly, we review the basic concepts and properties of black holes including AdS black holes. Then, we also elaborate the theories of Hawking radiation, thermodynamics laws and phase transition of black holes.In chapter2, we mainly describe the similarity of the critical behavior between in the Van der Waals model and in the AdS black hole. Firstly, we focus on elaborating the van der waals gas equation and the main critical properties in the Van der Waals system as the liquid-gas phase transition occurs. The critical point at where the first order phase transition happened is located at the endpoint of the coexistence line of the liquid-vapour equilibrium. The critical ratio pc=PcVc/Tc=3/8, and the corresponding critical exponents are a=0,β=1/2,γ=1and δ=3, respectively. Then, comparing the Van der Waals gas with the AdS black hole, we also elaborate the similarity of the critical properties including the critical exponents and the critical behavior in the phase transition between in the Van der Waals model and in the AdS black hole.In chapter3, We mainly study the thermodynamic properties of a charged AdS black hole in the special f(R) correction with the constant Ricci scalar curvature. Through treating the Ricci scalar curvature Ro as the cosmological constant and thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we analyze the critical exponents and the critical behavior in the AdS black hole in,f(R) gravity. We find that the f(R) correction influences the Gibbs free energy and the phase transition of system. The ratio pc occurring at the critical point increases monotonically with the derivative termf’(Ro). We also disclose that the critical exponents are the same as those of the liquid-gas phase transition in the Van der Waals model, which does not depend on the f(R) correction considered here.Finally, we present a summary and a outlook of the critical phenomena in the thermodynamics of AdS black hole.