Friday, January 28, 2011

Geometry for every solution of Navier-Stokes

Two weeks ago, I forgot to mention an exciting preprint,
From Navier-Stokes To Einstein
by Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, and - last but not least - Andrew Strominger. For every solution of the incompressible Navier-Stokes equations of hydrodynamics in "d" dimensions, they construct a canonical geometry that solves Einstein's equations in "d+2" equations. This geometry may be understood as a nonsingular perturbation of an event horizon.

This map is a rigorous doubly classical realization of a relationship between hydrodynamics and gravity that people have dreamed about for a long time.

The hydrodynamics expansion (a long-wavelength, non-relativistic expansion) of the Navier-Stokes solution turns out to be translated to the near-horizon expansion of the higher-dimensional geometry, including the non-linear contributions.

The fact that both sides of the relationship are classical solutions means that, in the AdS/CFT language, we're always focusing on phenomena that occur near the "center" of the bulk spacetime. However, you could argue that geometry becomes "hard" near the horizon - well, at least in some coordinates - which is why a dual, hydrodynamic representation has to exist.

I still haven't decided whether the relationship is a genuine profound physical insight - like other dualities - or just a bookkeeping device translating a set of fields into other fields.

Via Humble at the Physics Stack Exchange

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