An expedition to the islands of stability in the first-order causal hydrodynamics

TL;DR

This paper investigates the relationship between Lorentz invariance of stability and causality in first-order relativistic hydrodynamics, confirming that stability across reference frames depends on respecting signal propagation limits.

Contribution

It demonstrates that stability in different frames aligns with causality in a first-order relativistic hydrodynamic theory derived from kinetic equations.

Findings

Stability consistency across frames depends on causality.

The theory is microscopically derived from covariant kinetic equations.

Causality ensures stability in relativistic hydrodynamics.

Abstract

The recently proposed connection between the Lorentz invariance of stability and the speed of signal propagation has been tested for a first-order relativistic dissipative hydrodynamic theory. The fact that the stability situation in different reference frames agrees with each other only as long as the signal propagation respects causality, has been explicitly established for the theory, which is microscopically derived from the covariant kinetic equation in general hydrodynamic frames with arbitrary momentum-dependent interactions.