流体如何弯曲：高维黑洞的弹性膨胀
How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
摘要：
流体力学可以在背景时空中的任意余维表面上一致地表述，提供了描述黑膜长波长扰动的有效理论。当余维不为零时，系统获得流体弹性性质，并构成所谓的流体膜。应用有效作用量方法，在二阶导数展开下，构造了稳态流体膜构型的非本征曲率和非本征扭曲势的自由能二次函数的最一般形式.这种构造将理论生物学中研究的流体膜的Helfrich-Canham弯曲能推广到流体旋转的情况。研究发现，对于余维大于1的情况，静态流体膜构型的特征是一组3个弹性响应系数、3个流体动力学响应系数和1个自旋响应系数。此外，系统中存在的弹性自由度耦合到流体动力学自由度。对于余维-1曲面，我们发现了一个8个独立参数的稳态流体膜族。它进一步表明，弹性和自旋修正（非）-极值膜有效的行动可以占多极展开的应力-能量张量，因此建立了卡特，Capovilla-Guven和瓦西里-Vojinovic的不同形式主义之间的关系和重力和有效的描述之间的静态流体膜。最后，它表明，在文献中发现的黑色膜的杨氏模量属于这种方法预测的类-然后使用的关系，使一个建议的二阶有效行动的固定blackfolds和找到校正的地平线角速度薄的黑色环。
英文摘要：
Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.
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