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arXiv · 0809.4272

Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

Sayantani Bhattacharyya·R. Loganayagam·Ipsita Mandal·Shiraz Minwalla·Ankit Sharma
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Abstract

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength solutions of Einstein's equations with a negative cosmological constant, for all d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary d>2. We also rewrite the well known exact solutions for rotating black holes in AdS_{d+1} space in a manifestly fluid dynamical form, generalizing earlier work in d=4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

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Sayantani Bhattacharyya, R. Loganayagam, Ipsita Mandal, Shiraz Minwalla, Ankit Sharma. 2008-12-03. Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions. https://doi.org/10.1088/1126-6708%2F2008%2F12%2F116

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