8-13 August 2011
Rhode Island Convention Center
US/Eastern timezone

From Navier-Stokes to Einstein

12 Aug 2011, 16:20
20m
552 B (Rhode Island Convention Center)

552 B

Rhode Island Convention Center

Parallel contribution Field and String Theory Field and String Theory

Speaker

Ms Irene Bredberg (Harvard University)

Description

We discuss a mathematically precise realization of suggestions of a holographic duality relating fluids and spacetime horizons which began with the black hole membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence. Our explicit construction shows that every solution of the incompressible Navier-Stokes equation can be related to a solution of the vacuum Einstein equations. The fluid described by the Navier-Stokes equation in p+1 dimensions lives on the timelike boundary of the p+2 dimensional Einstein solution. We consider a "near-horizon" limit in which the boundary surface becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. Moreover, we discuss a connection to the Petrov classification of spacetimes in four dimensions (and its higher dimensional generalizations).

Summary

We discuss a holographic connection between the Navier-Stokes equation and the Einstein equations.

Primary author

Ms Irene Bredberg (Harvard University)

Co-authors

Andy Strominger (Harvard University) Cynthia Keeler (Harvard University) Vyacheslav Lysov (Harvard University)

Presentation Materials