Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-07-07
Phys.Lett.B711:411-416,2012
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, revtex4; v2: references added; v3 slightly shortened version published in PLB
Scientific paper
10.1016/j.physletb.2012.04.029
The dual fluid description for a general cutoff surface at radius r=r_c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter \epsilon, the coupled Einstein-Maxwell equations are solved up to O(\epsilon^2). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density \eta/s is independent of both the cutoff r_c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio \eta/s is independent of the cutoff r_c but dependent on the charge density of the black brane.
Ling Yi
Niu Chao
Tian Yu
Wu Xiao-Ning
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