Necessary conditions for causality from linearized stability at ultra-high boosts

TL;DR

This paper introduces a new method to determine necessary causality conditions in relativistic hydrodynamics by analyzing linear stability at high boosts, leveraging Lorentz invariance and a phenomenon called gamma-suppression.

Contribution

It presents a novel approach to constrain causal parameter space using linear stability analysis at non-zero momenta in boosted frames, applicable to hydrodynamic theories.

Findings

The method efficiently identifies causality constraints at near-luminal boosts.

Gamma-suppression suppresses higher-order terms at large boosts, simplifying analysis.

Validated in conformal Müller-Israel-Stewart theory, it remains within hydrodynamic validity.

Abstract

In this work, we provide a novel method to constrain the causal parameter space of a relativistic hydrodynamic system exclusively from its linear stability analysis at non-zero momenta. Our approach exploits the Lorentz-invariant stability property of causal theories. In boosted frames, the dispersion relation exhibits a feature that we call ``$\gamma$-suppression,'' whereby the higher-order terms in the wavenumber expansion are increasingly suppressed beyond leading order at large boosts. As a consequence, at near-luminal values of Lorentz boost, stability criteria at the spatially homogeneous limit are sufficient to identify the region of the parameter space that satisfies the necessary conditions of causality, even at non-zero momenta. After presenting the general hydrodynamic framework, we test the method in conformal M\"uller-Israel-Stewart theory and show that it provides an efficient way of deriving the necessary conditions of causality while remaining within the low-energy regime of hydrodynamic validity.