由黑洞膜动力学解不可压纳维-斯托克斯方程
The Incompressible Navier-Stokes Equations From Black Hole Membrane Dynamics
摘要：
研究了（d+2）维渐近Anti-de-Sitter时空中由黑膜事件视界定义的d+1时空维膜的动力学，证明了它可用d维不可压缩非相对论流体的纳维-斯托克斯方程描述.流体速度对应于水平线的法线，而流体能量的变化率等于负的水平线横截面积的变化率。分析是在膜范式方法黑洞，它适用于一般的非奇异零超曲面，提供了一个大规模的流体动力学极限存在。因此，我们发现，例如，Rindler加速视界的动力学也由不可压缩的纳维-斯托克斯方程描述。结果类似于Burgers方程和KPZ方程之间的关系，我们讨论了它的含义。
英文摘要：
We consider the dynamics of a d+1 space-time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de-Sitter space-time and show that it is described by the d-dimensional incompressible Navier-Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier-Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.
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