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arXiv 2008.00945gr-qc
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一般相对论耗散流体非线性方程的线性化

Linearizing a Non-linear Formulation for General Relativistic Dissipative Fluids

Thomas Celora, Nils Andersson, Greg L. Comer

备注：
Final version as published on Classical and Quantum Gravity
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摘要：

耗散广义相对论性多流体的完全非线性运动方程可以从包含明确使用低维物质空间的作用量原理得到。更传统的纳入耗散的策略--如著名的Mueller-Israel-Stewart模型--是基于偏离平衡的膨胀，部分由热力学热力学定律定义。这里的目标是建立一种形式，以便于将基于行动的结果与基于传统方法的结果进行比较。这个过程的第一步是使用基于行动的方法本身来构建自洽的平衡概念。接下来，一阶偏差直接在物质空间上发展，这促使后者成为基础热力学的自然舞台。最后，我们确定了基于行动的模型与一阶的“牺牲”通量，传统的模型是建立在耗散项。的描述是在一个一般的设置，使形式主义可以用来描述多流体系统，因果关系和稳定的模型还没有。作为一个例子的方法，一个简单的应用程序的一个单一的粘性流体被认为是，即使膨胀停止在一阶，我们素描如何因果响应可以通过Cattaneo型方程。

英文摘要：

Fully non-linear equations of motion for dissipative general relativistic multi-fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating dissipation-like the famous Mueller-Israel-Stewart model-are based on expansions away from equilibrium defined, in part, by the laws of thermodynamics. The goal here is to build a formalism to facilitate comparison of the action-based results with those based on the traditional approach. The first step of the process is to use the action-based approach itself to construct self-consistent notions of equilibrium. Next, first-order deviations are developed directly on the matter spaces, which motivates the latter as the natural arena for the underlying thermodynamics. Finally, we identify the dissipation terms of the action-based model with first-order "thermodynamical" fluxes, on which the traditional models are built. The description is developed in a general setting so that the formalism can be used to describe multi-fluid systems, for which causal and stable models are not yet available. As an illustration of the approach, a simple application of a single viscous fluid is considered and, even though the expansion is halted at first order, we sketch how a causal response can be implemented through Cattaneo-type equations.

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