According to the standard von Laue condition, the volume-averaged pressure inside particles of fixed mass and structure vanishes in the Minkowski limit of general relativity. Here we show that this condition is in general not fulfilled in the context of f(R,T) gravity, or of other theories of gravity in which the linear momentum is not conserved in this limit (here, R and T represent the Ricci scalar and the trace of the energy-momentum tensor, respectively). We derive a generalized von Laue condition valid for the R(R)+F(T) subclass of f(R,T) theories of gravity and discuss its cosmological implications. In particular, we show that the standard radiation and matter era evolution of the universe is recovered in the context R+F(T) gravity independently of the specific properties of the function F(T). We also find that dust — a perfect fluid whose particles are at rest in the fluid's proper frame — cannot in general be described as pressureless in the context of these theories. We further discuss the implications of our findings for the form of the on-shell Lagrangian of an ideal gas.

中文翻译：

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非平凡物质中的粒子及其流体扩展到广义相对论


根据标准的 von Laue 条件，固定质量和结构的粒子内部的体积平均压力在广义相对论的 Minkowski 极限中消失。在这里，我们表明，在 f（R，T） 引力或其他引力理论的背景下，线性动量在此极限内不守恒（这里，R 和 T 分别代表 Ricci 标量和能量-动量张量的轨迹），这个条件通常不满足。我们推导出了一个广义的冯·劳厄条件，该条件对 f（R，T） 引力理论的 R（R）+F（T） 子类有效，并讨论了它的宇宙学意义。特别是，我们表明，宇宙的标准辐射和物质时代演化是在 R+F（T） 引力的背景下恢复的，与函数 F（T） 的特定性质无关。我们还发现，尘埃——一种完美的流体，其粒子静止在流体的适当框架中——在这些理论的背景下，通常不能被描述为无压力。我们进一步讨论了我们的发现对理想气体的壳上拉格朗日形式的影响。