From Petrov-Einstein to Navier-Stokes
High Energy Physics - Theory
2011-06-06 v2 General Relativity and Quantum Cosmology
Fluid Dynamics
Abstract
We consider a p+1-dimensional timelike hypersurface \Sigma_c embedded with a flat induced metric in a p+2-dimensional Einstein geometry. It is shown that imposing a Petrov type I condition on the geometry reduces the degrees of freedom in the extrinsic curvature of \Sigma_c to those of a fluid in \Sigma_c. Moreover, expanding around a limit in which the mean curvature of the embedding diverges, the leading-order Einstein constraint equations on \Sigma_c are shown to reduce to the non-linear incompressible Navier-Stokes equation for a fluid moving in \Sigma_c.
Cite
@article{arxiv.1104.5502,
title = {From Petrov-Einstein to Navier-Stokes},
author = {Vyacheslav Lysov and Andrew Strominger},
journal= {arXiv preprint arXiv:1104.5502},
year = {2011}
}
Comments
Added references, discussion and appendix detailing alternate boundary conditions with fixed mean curvature