2006/05/02 by Nils Andersson, N. Andersson, G. L. Comer · 3 citations
Engineering · Physics and Astronomy · #Active galactic nucleus #Astrophysical jet #Astrophysics #Classical mechanics #Conservation law #Cosmology and Gravitation Theories #Equations of motion #Fluid Dynamics and Turbulent Flows #High-Energy Particle Collisions Research #Motion (physics) #Physics #Quantum mechanics #Theoretical physics #gr-qc
paper · pdf · doi:10.12942/lrr-2007-1
published as LivingRev.Rel.10:1,2005 · Invited review for Living Reviews in Relativity, 8 figures, uses livrevrel.bst, epubtk.sty
arxiv created 2006/05/02 · openalex publication_date 2007/01/30 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.