3+1 formulation of non-ideal hydrodynamics

TL;DR

This paper develops a 3+1 formulation of dissipative relativistic hydrodynamics using extended causal thermodynamics, applicable to arbitrary spacetimes and avoiding causality violations inherent in Navier-Stokes equations.

Contribution

It introduces a novel 3+1 framework for non-ideal hydrodynamics that incorporates dissipation via Israel-Stewart theory for arbitrary spacetimes.

Findings

Formulation applicable to stationary, axisymmetric spacetimes including Kerr metric

Simplified equations when dissipative inertia is negligible

Eliminates causality violations of traditional Navier-Stokes equations

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.