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

¹ Department of Mathematics, Vanderbilt University, Nashville TN, USA
² Department of Physics and Astronomy, Vanderbilt University, Nashville TN, USA
³ Instituto de Física, Universidade Federal Fluminense, Niterói, Brazil

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Published online: 17 April 2026

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 space-time 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.