Relativistic dissipative fluids in the trace-fixed particle frame: Hyperbolicity, causality, and stability

TL;DR

This paper develops a new first-order relativistic dissipative fluid theory in the trace-fixed particle frame, ensuring hyperbolicity, causality, and stability under certain conditions, with implications for modeling relativistic fluids.

Contribution

It introduces a novel first-order relativistic fluid theory in the trace-fixed particle frame that guarantees hyperbolicity and causality, extending previous models.

Findings

The theory is hyperbolic and causal if a specific inequality holds.

Expected damped modes are recovered at low wave numbers.

Global equilibrium stability is confirmed for certain gases.

Abstract

We propose a first-order theory of relativistic dissipative fluids in the trace-fixed particle frame, which is similar to Eckart's frame except that the temperature is determined by fixing the trace of the stress-energy tensor. Our theory is hyperbolic and causal provided a single inequality holds. For low wave numbers, the expected damped modes in the shear, acoustic, and heat diffusion channels are recovered. Stability of global equilibria with respect to all wave numbers is also analyzed. The conditions for hyperbolicity, causality and stability are satisfied for a simple gas of hard spheres or disks.