We present the first generalization of Navier-Stokes theory to relativity that satisfies all of the following properties: (a) the system coupled to Einstein’s equations is causal and strongly hyperbolic; (b) equilibrium states are stable; (c) all leading dissipative contributions are present, i.e., shear viscosity, bulk viscosity, and thermal conductivity; (d) nonzero baryon number is included; (e) entropy production is non-negative in the regime of validity of the theory; (f) all of the above hold in the nonlinear regime without any simplifying symmetry assumptions. These properties are accomplished using a generalization of Eckart’s theory containing only the hydrodynamic variables, so that no new extended degrees of freedom are needed as in Müller-Israel-Stewart theories. Property (b), in particular, follows from a more general result that we also establish, namely, sufficient conditions that when added to stability in the fluid’s rest frame imply stability in any reference frame obtained via a Lorentz transformation All of our results are mathematically rigorously established. The framework presented here provides the starting point for systematic investigations of general-relativistic viscous phenomena in neutron star mergers.

中文翻译：

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一阶广义相对论粘性流体动力学

我们将 Navier-Stokes 理论首次推广到满足以下所有性质的相对论：(b) 平衡状态是稳定的；(c) 存在所有主要的耗散贡献，即剪切粘度、体积粘度和热导率；(d) 包括非零重子数；(e) 熵产生在理论的有效性范围内是非负的；(f) 在没有任何简化对称假设的情况下，以上所有内容都适用于非线性状态。这些性质是使用仅包含流体动力学变量的 Eckart 理论的推广来实现的，因此不需要像 Müller-Israel-Stewart 理论中那样新的扩展自由度。财产（b），特别是，从我们也建立的更一般的结果得出，即，当添加到流体静止框架中的稳定性时，意味着在通过洛伦兹变换获得的任何参考系中的稳定性的充分条件我们所有的结果在数学上都是严格建立的。这里提出的框架为系统研究中子星合并中的广义相对论粘性现象提供了起点。