Non-boost invariant fluid dynamics
Non-boost invariant fluid dynamics
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非增压不变流体动力学
作者：
J. Boer;J. Hartong;Emil Have;N. Obers;W. Sybesma
我们认为不带电的流体没有任何提升对称性的任意弯曲的背景和分类所有允许的输运系数的一阶导数。我们假设旋转对称，我们使用熵流形式主义。在缺乏boost对称性的情况下，弯曲的背景几何被称为绝对时空或奥斯特时空。我们给出了朗道系中能量动量张量的封闭表达式，它分为三部分：耗散部分（10），流体静力非耗散部分（2）和非流体静力非耗散部分（4），其中括号中我们指出了允许的输运系数的数目。非流体静力学非耗散输运系数可以被认为是如果我们限制到线性化扰动并施加Onsager关系则会消失的系数的推广。对于两个流体静力学和四个非流体静力学非耗散输运系数，我们提出了拉格朗日描述。最后，当我们施加标度不变性，从而限制到Lifshitz流体，我们发现7耗散，1流体静力学和2非流体静力学非耗散传输系数。
We consider uncharged fluids without any boost symmetry on an arbitrary curved background and classify all allowed transport coefficients up to first order in derivatives. We assume rotational symmetry and we use the entropy current formalism. The curved background geometry in the absence of boost symmetry is called absolute or Aristotelian spacetime. We present a closed-form expression for the energy-momentum tensor in Landau frame which splits into three parts: a dissipative (10), a hydrostatic non-dissipative (2) and a non-hydrostatic non-dissipative part (4), where in parenthesis we have indicated the number of allowed transport coefficients. The non-hydrostatic non-dissipative transport coefficients can be thought of as the generalization of coefficients that would vanish if we were to restrict to linearized perturbations and impose the Onsager relations. For the two hydrostatic and the four non-hydrostatic non-dissipative transport coefficients we present a Lagrangian description. Finally when we impose scale invariance, thus restricting to Lifshitz fluids, we find 7 dissipative, 1 hydrostatic and 2 non-hydrostatic non-dissipative transport coefficients.