弱弯曲时空中的线性离散流体动力学
Linearly resummed hydrodynamics in a weakly curved spacetime
摘要：
本文将平坦空间~ \cite{1406.7222,1409.3095}中的全阶线性赋形流体动力学的研究推广到弱弯曲空间中的流体。基本的微观理论是在强耦合下的有限温度$\mathcal{N}=4$超杨-米尔斯理论。AdS/CFT对应关系将渐近\emph{locally} $\textrm{AdS}_5$几何中的爱因斯坦引力的黑膜解与弱弯曲4D背景中的相对论共形流体联系起来。对于流体动力学变量和度量扰动的振幅的线性阶，流体的能量-动量张量是用流体速度和背景度量的导数计算的。我们广泛地讨论了所有阶流体力学的意义，通过表示它的记忆函数形式主义，这也是适合于实际的模拟。除了文献[1]中详细讨论的两个粘度函数外，本文还讨论了两个粘度函数。\cite{1406.7222,1409.3095}，我们发现四个曲率诱导结构耦合到流体通过新的传输系数函数。参考文献~ \cite{0905.4069}，后者被称为流体的重力磁化率。我们分析计算这些系数的流体动力学限制，然后数值动量大的值。
英文摘要：
We extend our study of all-order linearly resummed hydrodynamics in a flat space~\cite{1406.7222,1409.3095} to fluids in weakly curved spaces. The underlying microscopic theory is a finite temperature $\mathcal{N}=4$ super-Yang-Mills theory at strong coupling. The AdS/CFT correspondence relates black brane solutions of the Einstein gravity in asymptotically \emph{locally} $\textrm{AdS}_5$ geometry to relativistic conformal fluids in a weakly curved 4D background. To linear order in the amplitude of hydrodynamic variables and metric perturbations, the fluid's energy-momentum tensor is computed with derivatives of both the fluid velocity and background metric resummed to all orders. We extensively discuss the meaning of all order hydrodynamics by expressing it in terms of the memory function formalism, which is also suitable for practical simulations. In addition to two viscosity functions discussed at length in refs.~\cite{1406.7222,1409.3095}, we find four curvature induced structures coupled to the fluid via new transport coefficient functions. In ref.~\cite{0905.4069}, the latter were referred to as gravitational susceptibilities of the fluid. We analytically compute these coefficients in the hydrodynamic limit, and then numerically up to large values of momenta.
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