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We study the linearized transport of transverse momentum and charge in aconjectured field theory dual to a black brane solution of Horava gravity withLifshitz exponent $z=1$. As expected from general hydrodynamic reasoning, wefind that both of these quantities are diffusive over distance and time scaleslarger than the inverse temperature. We compute the diffusion constants andconductivities of transverse momentum and charge, as well the ratio of shearviscosity to entropy density, and find that they differ from their relativisticcounterparts. To derive these results, we propose how the holographicdictionary should be modified to deal with the multiple horizons and differingpropagation speeds of bulk excitations in Horava gravity. When possible, as acheck on our methods and results, we use the covariant Einstein-Aetherformulation of Horava gravity, along with field redefinitions, to re-derive ourresults from a relativistic bulk theory.

Momentum and charge transport in non-relativistic holographic fluids from Ho\v{r}ava gravity