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

Abstract

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.

10 pages, no figures; v2: It turned out that even if a new term a_3(r) P dΩ_d^2 is added to the ansatz for the pressure-dependent part of the metric, eq (4), Einstein equation is still solvable. Then the deformed metric is parametrized by an arbitrary constant a_2. This new result is added. No changes in the conclusion. Typos are also corrected

References in corpus (3)

• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Nonlinear Fluid Dynamics from Gravity
• From Petrov-Einstein to Navier-Stokes

Cited by in corpus (3)

• Towards a general fluid/gravity correspondence
• Gravity-mediated holography in fluid dynamics
• Fluids and vortex from constrained fluctuations around C-metric black hole