3+1 formulation of non-ideal hydrodynamics

Abstract

The equations governing dissipative relativistic hydrodynamics are formulated within the 3+1 approach for arbitrary spacetimes. Dissipation is accounted for by applying the theory of extended causal thermodynamics (Israel-Stewart theory). This description eliminates the causality violating infinite signal speeds present in the conventional Navier-Stokes equation. As an example we treat the astrophysically relevant case of stationary and axisymmetric spacetimes, including the Kerr metric. The equations take a simpler form whenever the inertia due to the dissipative contributions can be neglected.Comment: 24 pages, LateX, uses mn.sty and AMS fonts, no figures, accepted for publication in the MNRAS, also available via http://www.lsw.uni-heidelberg.de/~jpeitz/Personal.htm