Fully non-linear equations of motion for dissipative general relativistic 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 build 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 "thermodynamic" fluxes, on which the traditional models are built. A simple application of a single viscous fluid is considered. The description is developed in a general setting so that the formalism can be used to describe more complicated systems, for which causal and stable models are not yet available. Finally, even though our expansions are halted at first order, we sketch out how a causal response can be implemented with telegraph-type equations.

中文翻译：

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线性化一般相对论耗散流体的非线性公式

耗散一般相对论流体的完全非线性运动方程可以从涉及显式使用低维物质空间的作用原理中获得。更传统的整合耗散策略（如著名的穆勒-以色列-斯图尔特模型）基于远离平衡的膨胀，部分由热力学定律定义。这里的目标是建立一种形式主义，以促进基于行动的结果与基于传统方法的结果的比较。该过程的第一步是使用基于行动的方法本身来建立自洽的均衡概念。接下来，直接在物质空间上发展一阶偏差，这促使后者成为潜在热力学的自然舞台。最后，我们用一阶“热力学”通量确定基于动作的模型的耗散项，传统模型建立在该模型上。考虑单一粘性流体的简单应用。该描述是在一般环境中开发的，因此形式主义可以用于描述更复杂的系统，对于这些系统，因果模型和稳定模型尚不可用。最后，即使我们的扩展在一阶停止，我们勾勒出如何用电报类型的方程实现因果响应。因果模型和稳定模型尚不可用。最后，即使我们的扩展在一阶停止，我们勾勒出如何用电报类型的方程实现因果响应。因果模型和稳定模型尚不可用。最后，即使我们的扩展在一阶停止，我们勾勒出如何用电报类型的方程实现因果响应。