# First-order relativistic hydrodynamics is stable

## TL;DR

This paper demonstrates that within the most general frame, certain conditions ensure the stability of first-order relativistic viscous hydrodynamics, challenging the necessity of extended theories like Israel-Stewart.

## Contribution

It identifies stable frames in first-order relativistic hydrodynamics and shows the Landau-Lifshitz frame is unstable, suggesting simpler variables may suffice for a consistent theory.

## Key findings

- Stable parameter regions exist for perturbations in relativistic viscous fluids.
- The Landau-Lifshitz frame is outside the stable region.
- First-order hydrodynamics can be stable without extended theories.

## Abstract

We study linearized stability in first-order relativistic viscous hydrodynamics in the most general frame. There is a region in the parameter space of transport coefficients where the perturbations of the equilibrium state are stable. This defines a class of stable frames, with the Landau-Lifshitz frame falling outside the class. The existence of stable frames suggests that viscous relativistic fluids may admit a sensible hydrodynamic description in terms of temperature, fluid velocity, and the chemical potential only, i.e. in terms of the same hydrodynamic variables as non-relativistic fluids. Alternatively, it suggests that the Israel-Stewart and similar constructions may be unnecessary for a sensible relativistic hydrodynamic theory.