Thirdorder relativistic hydrodynamics: dispersion relations and transport coefficients of a dual plasma
Abstract
Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the longwavelength and slowtime fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to third order in the gradient expansion for neutral fluids in a general curved spacetime of d dimensions. We find 58 new transport coefficients, 19 due to thirdorder scalar corrections and 39 due to tensorial corrections. In the particular case of a conformal fluid, the number of new transport coefficients is reduced to 19, all of them due to thirdorder tensorial corrections. The dispersion relations of linear fluctuations in the thirdorder relativistic hydrodynamics is obtained, both in the rest frame of the fluid and in a general moving frame. As an application we obtain some of the transport coefficients of a relativistic conformal fluid in three dimensions by using the AdS/CFT correspondence. These transport coefficients are extracted from the dispersion relations of the linear fluctuations. The gravity dual of the fluctuations in this conformal fluid is described by the gravitational perturbations of fourdimensional antide Sitter black branes, which are solutions of the Einstein equations with a negative cosmological constant. To find the hydrodynamic quasinormal modes (QNMs) of the scalar sector we use the SUSY quantum mechanics of the gravitational perturbations of fourdimensional black branes. Such a symmetry allows us to find the wavefunction of the scalar (or sound) sector in the hydrodynamic limit directly from the wavefunction of the vector (or shear) sector, which is usually easier to be found because the perturbation wave equations for the vector sector are much simpler than the ones for the scalar sector.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2020
 DOI:
 10.1007/JHEP05(2020)019
 arXiv:
 arXiv:1909.05199
 Bibcode:
 2020JHEP...05..019D
 Keywords:

 AdSCFT Correspondence;
 Black Holes;
 Classical Theories of Gravity;
 Holography and quarkgluon plasmas;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 41 pages, 1 figure