Nonlinear causality of general first-order relativistic viscous hydrodynamics
Nonlinear causality of general first-order relativistic viscous hydrodynamics
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DOI：
10.1103/physrevd.100.104020
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发表时间：
2019-07
影响因子：
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
有效的理论参数被用来推导出最一般的相对论粘性流体的能量-动量张量与任意状态方程（在没有其他守恒电流的情况下），这是一阶的能量密度和流速的导数，不包括扩展变量，如在穆勒-以色列-斯图尔特理论。这个能量-动量张量导致了一个因果理论，只要人们放弃了通常的惯例，由朗道-利夫希茨和埃卡特提出的平衡外的流体动力学变量。特别是，因果关系需要非零的平衡能量密度修正和热流。条件，以确保在平坦的时空平衡点附近的线性稳定性。我们还证明了运动方程解的局部存在唯一性。我们的因果关系，存在性和唯一性的结果持有在完整的非线性制度，没有对称性假设，在四个时空维度，有或没有耦合到爱因斯坦的方程，并在数学上严格建立。此外，还提供了该能量动量张量的动力学理论实现
Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero out-of-equilibrium energy density corrections and heat flow. Conditions are found to ensure linear stability around equilibrium in flat space-time. We also prove local existence and uniqueness of solutions to the equations of motion. Our causality, existence, and uniqueness results hold in the full nonlinear regime, without symmetry assumptions, in four space-time dimensions, with or without coupling to Einstein’s equations, and are mathematically rigorously established. Furthermore, a kinetic theory realization of this energy-momentum tensor is also provided