Towards a general fluid/gravity correspondence

Understand

We set up the construction of generic (d+2)-dimensional metrics corresponding to (d+1)-dimensional fluids, representing holographically the hydrodynamic regimes of the putative dual theories.

• We give general seed equilibrium metrics appropriate to generic bulk stress energy tensors and discuss the implications of conformal rescalings of the hypersurface on which the fluid is defined.
• We then show how to obtain the corresponding hydrodynamic metrics using a relativistic gradient expansion and discuss the integrability conditions of the resulting equations.
• The stress energy tensors of the resulting fluids, both at and away from equilibrium, satisfy a quadratic constraint.