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

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.