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Petrov type $I$ condition and dual relativistic fluid dynamics

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Co-authors: Rong-Gen Cai (Institute of Theoretical Physics, Chinese Academy of Sciences), Kostas Skenderis (University of Southampton)

It has been shown that imposing a Petrov type $I$ condition on a $(p+1)$-dimensional timelike hypersurface embedded in a $(p+2)$-dimensional vacuum Einstein gravity reduces the degrees of freedom in the extrinsic curvature of the hypersurface to that of a fluid on the hypersurface. We show that the Relativistic fluid dual to vacuum Einstein gravity does satisfy the covariant Petrov type $I$ condition at least up to second order in derivative expansion. In addition, we show that this procedure can be inversed to derive the relativistic hydrodynamics with higher order corrections through imposing the Petrov type $I$ condition, and that some second order transport coefficients can also be extracted.

Coset model for the Luttinger liquid

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