Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-06
JHEP 0903:120,2009
Physics
High Energy Physics
High Energy Physics - Theory
17 pages
Scientific paper
10.1088/1126-6708/2009/03/120
We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are analyzed. We construct exact solutions with finite time singularities of one-dimensional relativistic conformal hydrodynamic motions, and use them to generate multi-dimensional solutions via special conformal transformations. These solutions, however, are shown to have no non-trivial slow motions limit. A simple non-equilibrium steady state in the form of a shock solution is constructed, and its inner structure is analyzed. We demonstrate that the derivation of the gravitational dual description of conformal hydrodynamics is analogous to the derivation of hydrodynamics equations from the Boltzmann equation. The shock solution is shown to correspond to a domain-wall solution in gravity. We show that the solutions to the non-relativistic incompressible Navier-Stokes equations play a special role in the construction of global solutions to gravity.
Fouxon Itzhak
Oz Yaron
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