The Holographic Fluid on the Sphere Dual to the Schwarzschild Black Hole

Details The Holographic Fluid on the Sphere Dual to the Schwarzschild Black Hole The Holographic Fluid on the Sphere Dual to the Schwarzschild Black Hole

2011-09-06

arxiv.org/abs/1109.1185v2

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, no figures; v2: It turned out that even if a new term a_3(r) P d\Omega_d^2 is added to the ansatz for the pressure-d

Scientific paper

We consider deformation of the d+2 dimensional asymptotically flat Schwarzschild black hole spacetime with the induced metric on a d-sphere at $r=r_c$ held fixed. This is done without taking the near horizon limit. The deformation is determined so that the $\Lambda=0$ vacuum Einstein equation is satisfied and the metric is regular on the horizon. In this paper the velocity of a dual fluid $v^i$ is assumed to be a Killing field and small, and the deformed metric is obtained up to $O(v^2)$. At this order of hydrodynamic expansion the dual fluid is an ideal one. The structure of the metric is fairly different from the near horizon result of Bredberg and Strominger in arXiv:1106.3084.

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