Causality constraints and anisotropic states

TL;DR

This paper explores how anisotropy influences dispersion relations and convergence in relativistic hydrodynamics, revealing a continuum of mode collisions and establishing bounds on the convergence radius based on causality constraints.

Contribution

It demonstrates the presence of a continuum of hydrodynamic mode collisions in anisotropic systems and provides criteria for their impact on the hydrodynamic expansion's convergence.

Findings

Continuum of collisions between hydrodynamic modes at complex wavevector

Presence of these collisions in holographic plasma models

Upper bound on the convergence radius based on causality

Abstract

We investigate the effects of anisotropy on dispersion relations and convergence in relativistic hydrodynamics. In particular, we show that for dispersion relations with a branch point at the origin (such as sound modes), there exists a continuum of collisions between hydrodynamic modes at complex wavevector. These collisions are then explicitly demonstrated to be present in a holographic plasma. We lay out a criterion for when the continuum of collisions affects the convergence of the hydrodynamic derivative expansion. Finally, the radius of convergence of hydrodynamic dispersion relations in anisotropic systems is bounded from above on the basis of compatibility with microscopic causality.