【作者】 张伟；

【导师】 凌意；

【作者基本信息】 南昌大学 ， 天体物理， 2014， 硕士

【摘要】 最近，引力的全息性质的研究取得了很大的进展。全息引力的一个重要的研究方向是引力/流体对偶的研究，也是当前国际研究的一个热点课题。利用超曲面的Petrov-like边界条件可以在近视界极限下将描述引力的Einstein场方程约化为低一维时空中的描述流体的Navier-Stokes方程。然而，此前这种方法有一个明显的不足，那就是所建立的引力/流体对偶只适用于近视界极限情况。在本论文中，我们将在Petrov-like框架下采用一种全新的方法,用长波极限替代近视界极限，从而在距视界为有限距离的任意截面上都能建立引力/流体对偶。具体来说，我们构建了三个精确的模型。第一，通过在Rindler时空中的任意有限截面施加Petrov-like边界条件并采用长波极限的方法，由Einstein场方程推导出了流体Navier-Stokes方程；第二，将同样的方法运用到带宇宙学常数的黑膜时空，我们也得到了Navier-Stokes方程,并且得到粘滞系数与截断坐标间的依赖关系；最后，考虑一个有物质场的4维带磁荷的黑膜时空，我们也同样可以建立引力/流体的对偶关系。更多还原

【Abstract】 Recently great progress has been made in disclosing the holographic nature ofgravity. One important direction of the holographic gravity is the study ofgravity/fluid duality, which has also been becoming a hot topic in the frontier of thecurrent international research.It has been shown that imposing Petrov-like boundary condition on ahypersurface may reduce the Einstein equation of gravity to the incompressibleNavier-Stokes equation of fluid in one lower dimensional spacetime in thenear-horizon limit. However, the method of imposing Petrov-like boundary conditionpreviously contains an obvious weak point. That is, the gravity/fluid duality can beestablished only in the near-horizon limit.In this thesis, we will employ the new method of the long-wavelength limitinstead of the near-horizon limit under the Petrov-like framework, and construct agravity/fluid duality at an arbitrary finite cutoff surface. In particular, we constructthree explicit models. Firstly, we derived the Navier-Stokes equation from theEinstein equation in Rindler spacetime by imposing the Petrov-like boundarycondition on an arbitrary finite cutoff surface and employing the long-wavelengthlimit. Secondly, we applied the same method to a black brane spacetime which has acosmological constant, and the Navier-Stokes equation of fluid with acutoff-dependent viscosity can be derived. Lastly, a4-dimensional magnetic blackbrane spacetime which has matter fields is considered, and the gravity/fluid dualitycan be established as well.更多还原