The holographic fluid dual to vacuum Einstein gravity

By G. Compère, Paul McFadden, Kostas Skenderis, Marika Taylor. 2011

135 citations recorded by the source corpus.

We present an algorithm for systematically reconstructing a solution of the (d + 2)-dimensional vacuum Einstein equations from a (d + 1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al. in arXiv:1101.2451 to arbitrary order. The fluid satisfies equations of motion which are the incompressible Navier-Stokes equations, corrected by specific higher-derivative terms. The uniqueness and regularity of this solution is established to all orders and explicit results are given for the bulk metric and the stress tensor of the dual fluid through fifth order in the hydrodynamic expansion. We establish the validity of a relativistic hydrodynamic description for the dual fluid, which has the unusual property of having a vanishing equilibrium energy density. The gravitational results are used to identify transport coefficients of the dual fluid, which also obeys an interesting and exact constraint on its stress tensor. We propose novel Lagrangian models which realise key properties of the holographic fluid.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dc86d26f2f787b5ad7b889e3a2bcf25555b2920f

Citations in the corpus

• TT deformations in general dimensions (2018, unknown): “6) In the case of flat space in Rindler coordinates, the stress tensor on a hypersurface Σc indeed takes the perfect fluid form, with [19, 20] p = 4πTU + C ρ = −C (7.”