Vol. 10 (2007) > lrr-2007-1

doi: 10.12942/lrr-2007-1
Living Rev. Relativity 10 (2007), 1

Relativistic Fluid Dynamics: Physics for Many Different Scales

1 School of Mathematics, University of Southampton, Southampton SO17 1BJ, U.K.
2 Department of Physics & Center for Fluids at All Scales, Saint Louis University, St. Louis, MO, 63156-0907, U.S.A.

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Article Abstract

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as ``small'' as heavy ions in collisions, and as large as the Universe itself, with ``intermediate'' sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the ``standard'' text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an ``integrability'' condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.

Keywords: fluid dynamics, relativistic hydrodynamics, relativistic astrophysics, variational methods, classical field theory

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

Nils Andersson and Gregory L. Comer,
"Relativistic Fluid Dynamics: Physics for Many Different Scales",
Living Rev. Relativity 10,  (2007),  1. URL (cited on <date>):
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Article History

ORIGINAL http://www.livingreviews.org/lrr-2007-1
Title Relativistic Fluid Dynamics: Physics for Many Different Scales
Author Nils Andersson / Gregory L. Comer
Date accepted 12 January 2007, published 30 January 2007
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