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arXiv 1201.2678hep-thgr-qc
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相对论性流体与真空的对偶爱因斯坦引力

The relativistic fluid dual to vacuum Einstein gravity

Geoffrey Compère, Paul McFadden, Kostas Skenderis, Marika Taylor

备注：
29 pages, 1 figure; v2: added comments and references, published version
发表信息：
JHEP 03(2012)076
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摘要：

我们提出了一个（d+2）维的Ricci平坦度规对应的（d+1）维相对论流体，全息代表（假定）的对偶理论的流体力学制度的建设。我们展示了如何使用相对论梯度展开获得任意高阶的度量，并明确地进行计算到二阶。流体在平衡时具有零能量密度，这意味着梯度中的一阶不可压缩性，并且其应力张量（在平衡处和远离平衡处）满足二次约束，这决定了其远离平衡的能量密度。整个动力学二阶编码在一个一阶和六个二阶传输系数，我们计算。我们在相对论梯度中对具有非负发散的二阶熵流进行了分类。然后，我们验证了通过拉回到流体表面的面积形式在零视界的熵流确实有一个非负的发散。我们发现，有明显的近地平线标度限制，是等价于我们在这里讨论的相对论梯度展开，或与纳维-斯托克斯方程在以前的工作中讨论的非相对论性的扩展。后一种膨胀可以在取一个特定的非相对论性极限时从当前的相对论性膨胀中恢复。

英文摘要：

We present a construction of a (d+2)-dimensional Ricci-flat metric corresponding to a (d+1)-dimensional relativistic fluid, representing holographically the hydrodynamic regime of a (putative) dual theory. We show how to obtain the metric to arbitrarily high order using a relativistic gradient expansion, and explicitly carry out the computation to second order. The fluid has zero energy density in equilibrium, which implies incompressibility at first order in gradients, and its stress tensor (both at and away from equilibrium) satisfies a quadratic constraint, which determines its energy density away from equilibrium. The entire dynamics to second order is encoded in one first order and six second order transport coefficients, which we compute. We classify entropy currents with non-negative divergence at second order in relativistic gradients. We then verify that the entropy current obtained by pulling back to the fluid surface the area form at the null horizon indeed has a non-negative divergence. We show that there are distinct near-horizon scaling limits that are equivalent either to the relativistic gradient expansion we discuss here, or to the non-relativistic expansion associated with the Navier-Stokes equations discussed in previous works. The latter expansion may be recovered from the present relativistic expansion upon taking a specific non-relativistic limit.

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