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The Navier–Stokes equation and solution generating symmetries from holography

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Abstract

The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess solution-generating symmetries known as spacetime Ehlers transformations. These form a subgroup of the larger generalized Ehlers group acting on spacetimes with arbitrary matter content. We apply this generalized Ehlers group, in the presence of Killing isometries, to vacuum metrics with hydrodynamic duals to develop a formalism for solution-generating transformations of incompressible Navier–Stokes fluids. Using this we provide examples of a linear energy scaling from RG flow under vanishing vorticity, and a set of \( {{\mathbb{Z}}_2} \) symmetries for fixed viscosity.

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Authors and Affiliations

  1. Queen Mary University of London, Centre for Research in String Theory, School of Physics, Mile End Road, London, E1 4NS, U.K.

    Joel Berkeley & David S. Berman

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  1. Joel Berkeley
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  2. David S. Berman
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Correspondence to David S. Berman.

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ArXiv ePrint: 1211.1983

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Berkeley, J., Berman, D.S. The Navier–Stokes equation and solution generating symmetries from holography. J. High Energ. Phys. 2013, 92 (2013). https://doi.org/10.1007/JHEP04(2013)092

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