The Studies On Holographic And Thermodynamic Properties Of Gravity

As the most successful realization of the holographic principle, Anti-de Sit-ter/Conformal Field Theory (AdS/CFT) correspondence, which relates a string the-ory in AdS spacetime to a conformal field theory living on its boundary, has provided a method to study the strong coupled field theories in a weakly coupled dual gravita-tional description. In modern condensed matter physics, one of the unsolved myster-ies is the core mechanism governing the high-temperature superconductor systems which are not described by the usual BCS theory. In recent years, the AdS/CFT correspondence has been applied to study the condensed matter physics in order to understand the physics of high superconductors from the gravitational dual. Besides, there have been accumulated interest to study black hole thermodynamics which is an intersectional field of general relativity, thermodynamics, quantum mechanics, and so on. These studies help us to understand gravity and thermodynamics. The holographic superconductors and black hole thermodynamics are studies as follows:We analytically investigate the phase transition between the holographic insu-lator and superconductor with Weyl corrections by using the variational method for the Sturm-Liouville eigenvalue problem. We find that similar to the curva-ture corrections, in p-wave model, the higher Weyl couplings make the insula-tor/superconductor phase transition harder to occur. However, in s-wave case the Weyl corrections do not influence the critical chemical potential, which is in con-trast to the effect caused by the curvature corrections. Moreover, we observe that the Weyl corrections will not affect the critical phenomena and the critical exponent of the system always takes the mean-field value in both models. Our analytic results are found to be in good agreement with the numerical findings.We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear elec-trodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency. However, in strong contrast to the influence of the curvature correction, we find that in the AdS soliton background the nonlinear electrodynamics correction will not affect the properties of the holographic insulator and superconductor phase transitions, which may be a quite general feature for the s-wave holographic insulator/superconductor system.We investigate the effect of the RF2 correction on the holographic supercon-ductor model in the background of AdS black hole. We observe that, similar to the effect caused by the Weyl correction, the higher RF2 correction term can make it easier for the scalar operator to condense and result in the larger deviation from the expected relation in the gap frequency. However, we find that the condensation gap becomes larger as the RF2 correction term increases, which is in strong contrast to the influences of the Weyl correction and Gauss-Bonnet correction.We employ the matching method to analytically investigate the holographic superconductors with Lifshitz scaling in an external magnetic field. We discuss systematically the restricted conditions for the matching method and find that this analytic method is not always powerful to explore the effect of external magnetic field on the holographic superconductors unless the matching point is chosen in an appropriate range and the dynamical exponent z satisfies the relation z =d - 1 or z= d - 2. From the analytic treatment, we observe that Lifshitz scaling can hinder the condensation to be formed, which can be used to back up the numerical results. Moreover, we study the effect of Lifshitz scaling on the upper critical magnetic field and reproduce the well-known relation obtained from Ginzburg-Landau theory.For a thermodynamic system with multiple pairs of intensive/extensive vari-ables and the thermodynamical coefficients attain finite or infinite values on the phase boundary, we obtain the two classes of Ehrenfest equations in the full phase space, and find that the rank of the matrix for these equations can tell us the di-mensions of the phase boundary. We also apply this treatment to the RN-AdS black hole and study the thermodynamic properties of the RN-AdS black hole in full phase space. We propose a generalized thermodynamic identity and find a re-lation of thermodynamical coefficients between the grand canonical and canonical ensembles. We shown that the Stokes theorem indicates a general "oscillating" part (theoretical curve) can be replaced by a complicated actual evolution curve for the first order phase transition.