空间弯曲时空中的从Petrov-Einstein到Navier-Stokes
From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime
摘要：
我们将arXiv：1104.5502中的框架推广到嵌入可能具有非零内在曲率的情况。直接采用Brown-York应力张量作为基本变量，我们研究了在保持内度量不变的情况下，外曲率的有限扰动的影响。我们表明，施加彼得罗夫I型条件的超曲面几何可以减少到不可压缩的纳维-斯托克斯方程的流体运动在空间弯曲的时空在近地平线的限制。
英文摘要：
We generalize the framework in arXiv:1104.5502 to the case that an embedding may have a nonvanishing intrinsic curvature. Directly employing the Brown-York stress tensor as the fundamental variables, we study the effect of finite perturbations of the extrinsic curvature while keeping the intrinsic metric fixed. We show that imposing a Petrov type I condition on the hypersurface geometry may reduce to the incompressible Navier-Stokes equation for a fluid moving in spatially curved spacetime in the near-horizon limit.
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