Some Research On The Gravitational Solutions And The Corresponding Properties

In this thesis we do some research on solving the gravitational solutions and the corresponding thermodynamic or holographic properties.Investigations on black hole thermodynamics reveal the relations between gravity and thermodynamics,which indicates that black holes have thermodynamic properties and is an important evidence for holographic principle.AdS/CFT correspondence is a kind of realization for this conjecture.It creates new links between gauge theories and gravitational theories and provides new tools for solving problems in theoretical physics.dRGT massive gravity is a gravitational theory considering the non-vanishing mass of the graviton and has been proved to be well-defined.Due to this research background,we first derive a series of generalized Vaidya-like solutions and then investigate the corresponding thermodynamics.Utilizing the unified first law,we find that the Misner-Sharp mass is well-defined in this dynamical space-time.Furthermore,the Clausius relation is satisfied on the apparent horizon.Therefore,the unified first law on the apparent horizon can be written as the first law of thermodynamics using the Clausius relation.Finally,we verify that the Misner-Sharp mass is always well-defined for the dynamical space-time with a maximally symmetric subspace and we also give the covariant form for it.The rest of the thesis concentrates on the investigation of the fluid/gravity correspondence which is a kind of applications of AdS/CFT correspondence.By perturbing the Schawarzschild-AdS black brane background using the well-known methods from fluid/gravity correspondence,one can obtain the Einstein equations to the first order.On the other hand,according to the AdS/CFT correspondence,one can obtain the stress tensor to the first order for the dual fluid on the finite cutoff surface.After taking several sets of gauge and boundary conditions into consideration,we notice that the different stress tensors are in the same form.So we investigate the relation among the stress tensor to the first order,the Einstein equations and the boundary conditions for the first order dual fluid and we prove that actually there is a universal relation which we call universality.Furthermore,this universality can be generalized to the case where the bulk is set to be the perturbed charged RN-AdS black brane.