In this project, at first we calculate the horizon radius in both isotropic and anisotropic universes. Then we use this radius to calculate the horizon temperature. We obtained an anisotropic temperature. Moreover, we study thermodynamic geometry for pure Lovelock black holes and derive its thermodynamic curvature singularities. The thermodynamic scalar curvature determines the interaction of microstates whether it is repulsive or attractive. Also, we calculate thermodynamic extrinsic curvature and compare it with other thermodynamic variables. Moreover, we determine the order of phase transition by using the Ehrenfest’s equations and the Prigogine-Defay ratio. We investigate the critical behavior and the thermodynamic geometry of pure Lovelock black holes for various dimensions in the extended phase space. In the last chapter, we obtain the Friedmann equations of the universe in two gravity theories i.e. quartic quasi-topological and pure Lovelock. Using Hawking temperature relation at the apparent horizon of Friedmann Robertson Walker (FRW) universe, we eva‎luate associated entropy. In the following, by establishing the first law of thermodynamic on the apparent horizon we subsequently derive the generalized form of the Freidmann equations. We use dynamical system analysis to investigate quartic quasi-topological and the pure Lovelock theories.

بهروز ميرزا

احمد شيرزاد

مسلم زارعي، غلامرضا خسروي