First-Order General-Relativistic Viscous Fluid Dynamics
First-Order General-Relativistic Viscous Fluid Dynamics
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DOI：
10.1103/physrevx.12.021044
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发表时间：
2020-09
影响因子：
12.5
通讯作者：
F. S. Bemfica;M. Disconzi;J. Noronha
中科院分区：
文献类型：
--
作者：
F. S. Bemfica;M. Disconzi;J. Noronha
我们提出了Navier-Stokes理论对相对论的第一个推广，它满足以下所有性质：(a)与爱因斯坦方程耦合的系统是因果的和强双曲的；(b)平衡态稳定；(c)所有主要耗散贡献都存在，即剪切粘度、体粘度和导热性；(d)包含非零重子数；(e)在理论的有效性范围内，熵产是非负的；(f)在不作任何简化对称假设的非线性条件下，上述条件均成立。这些性质是通过对Eckart理论的推广来实现的，该理论只包含流体动力变量，因此不需要像m<s:1> ller- israel - stewart理论那样需要新的扩展自由度。特别是性质(b)，是由我们还建立的一个更一般的结果得出的，即，当加上流体在静止系中的稳定性时，就意味着在通过洛伦兹变换得到的任何参考系中的稳定性的充分条件。我们所有的结果都是在数学上严格建立起来的。本文提出的框架为系统地研究中子星合并中的广义相对论粘性现象提供了起点。
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) non-zero baryon number is included; (e) entropy production is non-negative in the regime of validity of the theory; (f) all of the above holds 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 our results are mathematically rigorously established. The framework presented here provides the starting point for systematic investigations of generalrelativistic viscous phenomena in neutron star mergers.