Based on the observations that there exists an analogy between the Reissner-Nordström-anti-de Sitter (RN-AdS) black holes and the van der Waals-Maxwell liquid-gas system, in which a correspondence of variables is (φ, q) ↔ (V, P ), we study the Ruppeiner geometry, defined as Hessian matrix of black hole entropy with respect to the internal energy (not the mass) of black hole and electric potential (angular velocity), for the RN, Kerr and RN-AdS black holes. It is found that the geometry is curved and the scalar curvature goes to negative infinity at the Davies' phase transition point for the RN and Kerr black holes.Our result for the RN-AdS black holes is also in good agreement with the one about phase transition and its critical behavior in the literature.

Using the recently obtained holographic cosmic duality, we reached a reasonable quantitative agreement between predictions of the Cosmic Microwave Background Radiation at small l and the WMAP observations, showing the power of the holographic idea. We also got constraints on the dark energy and its behaviour as a function of the redshift upon relating it to the small l CMB spectrum. For a redshift independent dark energy, our constraint is consistent with the supernova results, which again shows the correctness of the cosmic duality prescription. We have also extended our study to the redshift dependence of the dark energy.

We reexamined the argument that the quasinormal modes could be a probe of the phase transition of a topological black hole to a hairy configuration by investigating general scalar perturbations. We found further evidence in the quasinormal modes for this phase transition. For the general black hole configurations, we observed that although the quasinormal modes can present us different phases of different configurations, it is not powerful to disclose the phase transition at the critical point.

Employing the Quark Mass Denisity-and temperature-dependent model and the Hartle's method, We have studied the slowly rotating strange star with uniform angular velocity. The mass-radius relation, the moment of inertia and the frame dragging for different frequencies are given. We found that we cannot use the strange star to solve the challenges of Stella and Vietri for the horizontal branch oscillations and the moment of inertia I 45 /(M/M s ) > 2.3. Furthermore, we extended the Hartle's method to study the differential rotating strange star and found that the differential rotation is an effective way to get massive strange star.

We have studied the wave dynamics and the Hawking radiation for the scalar field as well as the brane-localized gravitational field in the background of the braneworld black hole with tidal charge containing information of the extra dimension. Comparing with the four-dimensional black holes, we have observed the signature of the tidal charge which presents the signals of the extra dimension both in the wave dynamics and the Hawking radiation.