Some Holographic Investigations Of Gravity And Cosmology

In 1970’s,Bekenstein studied black hole physics and found that its entropy was proportional to the area of black hole horizon,instead of the volume of black hole.It is very different from a well-known fact in Thermodynamics and Statistical Physics,which tells us that the entropy in a physical system should be proportional to the volume of the system.Bekenstein’s work first shed an insightful light on holography.The holographic concept plays an important role on the modern physics,and changes dramatically the viewpoints for physical phenomenons.The main idea of holographic principle is that in a physical system the degrees of freedom in bulk can be fully encoded by ones at boundary,vice versa.Based on holographic principle,one has successfully established gauge/gravity duality.This duality is the most important realization of holographic principle,which tells us that the degrees of freedom of gravity(quantum gravity)in anti de Sitter space are equivalently described by the degrees of freedom of quantum field theory at the boundary in one lower dimension.It has been applied extensively to study the hydrodynamical behavior of gravity and the quantum computational complexity for the holographic boundary state.Furthermore,using the holographic principle,theorists have successfully established the entropy force models to describe our universe.In this dissertation,in the holographic method,we mainly have investigated some topics on fluid/gravity duality,holographic complexity and the singularity of the early universe,respectively.The corresponding conclusions have been presented as follow:In Chapter 2 and Chapter 3,under the nonrelativistic and the near horizon limits,keeping the induced metric on the timelike hypersurface fixed and taking Brown-York tensor as the fundamental variables,imposing the Petrov-like boundary condition on the hypersurface,we found that the near-horizon dynamics of the Einstein–Dilaton–Axion and massive gravity theories in bulk can be fully governed by the incompressible Navier-Stokes equations moving on the hypersurface in one lower dimension,such that the holo-graphic nature and elegant of the Petrov-like boundary condition have been testified further.In our two cases,in spite of taking the effect of spacetime anisotropy and one of graviton mass terms into account,respectively,the ratios of the dynamical shear viscosity to entropy density in dual fluids still are 1/4π,which means that they both still saturate KSS bound.Furthermore,in some literature,although the effect of anisotropy and one of graviton mass terms are considered,their ratios of dynamical shear viscosity to entropy density also satisfy the KSS bound.These suggest that our results are consistent with their corresponding results.In Chapter 4,we mainly try to give out the relation of holographic complexity in the context of massive gravity and discuss what the role for the graviton mass terms can play.According to the duality between holographic quantum complexity and classical action of gravity,under the late time limit,we have computed the classical action growth rates for various massive AdS black holes in the WDW patch,and found that for the neutral massive AdS black hole computers,their computational speeds are the same as ones for the corresponding neutral AdS black hole computers,which in the cases are independent with the graviton mass terms;for the charged massive AdS black holes computers,their computational speeds are always superior to ones for those corresponding black hole computers without the graviton mass terms.This has suggested that the graviton mass terms play an important role in improving the computational speed in the charged black hole computers.In Chapter 5,employing the modified dispersion relation and Clausius relation,we have derived the general modified Friedmann equations and the corresponding modified entropy-area relations for the Friedmann-Robertson-Walker(FRW)Universe,and also discussed their corresponding behaviors in the bouncing scenario.In this setup,we find that the bouncing behaviors can appear in the flat and closed universes.The difference between them is that when bouncing behavior for the flat universe is presented,the entropy-area relation is negative;then when bouncing behavior for the closed Universe is in presence,the corresponding entropy-area relation is just zero.Surprisingly,for the open universe,the bouncing behavior is in absence.This has suggested that the bouncing behaviors for our universe and the corresponding entropy-area relations both are sensitive to the topology of the universe.In the last chapter,we give out the conclusions and some outlook in this dissertation.