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Within the context of the AdS/CFT correspondence we show that the DC thermoelectric conductivity can be obtained by solving the linearised, time-independent and forced Navier-Stokes equations on the black hole horizon for an incompressible and charged fluid.
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In general, the result η = s / 4 π \eta=s/4\pi will not be valid for translationally invariant anisotropic black holes nor for holographic lattices
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For simplicity we have set 16 π G = 1 16\pi G=1 and also set the cosmological constant to a convenient value
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The time dependent piece in ( 21
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2015
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