What happens in hydrodynamic simulations of heavy-ion collisions when causality is violated?

TL;DR

This paper investigates how violations of causality in relativistic hydrodynamic simulations of heavy-ion collisions lead to instabilities, classifying regions by their causal and stability properties and comparing numerical results with analytical solutions.

Contribution

It provides a detailed analysis of causality violations in Israel-Stewart hydrodynamics, classifies spacetime regions, and demonstrates instability development through simulations.

Findings

Causality violations can cause numerical and analytical instabilities.

Classification of spacetime regions into causal/stable, acausal/stable, and acausal/unstable.

Comparison of MUSIC solver predictions with analytical solutions shows instability development.

Abstract

We summarize our recent investigations on how causality violations in Israel-Stewart-type relativistic viscous hydrodynamic simulations can give rise to both analytical and numerical instabilities. The classification of spacetime regions into causal and stable ("good"), acausal but stable ("bad"), and acausal and unstable ("ugly") is reviewed. We compare the predictions of the MUSIC hydrodynamic solver with an analytical solution, and demonstrate how the acausality-driven instabilities develop in a simple one-dimensional scenario.