We show how causal relativistic Navier-Stokes equations arise from the relativistic Boltzmann equation: the causality is preserved via a judicious choice of the zero modes of the collision operator. A completely analogous procedure may be used to extract causal hydrodynamics from the fluid-gravity correspondence: again, causality of the hydrodynamic equations is preserved by a suitable choice of zero modes of the corresponding differential operators in the bulk. We give examples of zero modes which give rise to causal hydrodynamic equations for nonconformal fluids with a conserved U(1) global symmetry current.

中文翻译：

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来自动力学理论和全息术的因果一阶流体动力学

我们展示了因果相对论 Navier-Stokes 方程是如何从相对论 Boltzmann 方程产生的：通过对碰撞算子的零模式的明智选择来保持因果关系。可以完全类似的过程从流体 - 重力对应关系中提取因果流体动力学：同样，通过合适的选择，整体中相应的差分运算符的零模式可以保留流体动力方程的因果关系。我们给出了零模式的例子，这些例子产生了具有守恒 U(1) 全局对称电流的非保形流体的因果流体动力学方程。