Nonlinear fluid dynamics from gravity
Nonlinear fluid dynamics from gravity
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DOI：
10.1088/1126-6708/2008/02/045
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发表时间：
2007-12
影响因子：
5.4
通讯作者：
Sayantani Bhattacharyya;V. Hubeny;Shiraz Minwalla;Mukund Rangamani
中科院分区：
文献类型：
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作者：
Sayantani Bhattacharyya;V. Hubeny;Shiraz Minwalla;Mukund Rangamani
AdS5 中的黑色膜出现在由速度和温度标记的四参数族中。将这些参数推广到戈德斯通模式或集体坐标场（AdS5 边界上坐标的任意函数），我们使用爱因斯坦方程以及正则性要求和边界条件来确定它们的动力学。由此产生的方程是边界流体动力学方程，具有流体参数的特定值。我们的分析在边界导数展开中是扰动的，但对于任意幅度是有效的。我们的工作可以被视为边界流体动力学非线性方程从重力的推导。作为具体应用，我们找到了该流体应力张量展开的显式表达式，包括导数展开中高达二阶的项。
Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields—arbitrary functions of the coordinates on the boundary of AdS5—we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.