Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics
Ian Cordeiro, Fábio S. Bemfica, Enrico Speranza, Jorge Noronha
TL;DR
This work addresses nonlinear causality and local well-posedness in Israel-Stewart hydrodynamics with bulk and shear viscosity and a nonzero baryon current. By casting the equations into a first-order quasilinear form and performing characteristic analysis, the authors derive algebraic, necessary-and-sufficient conditions for nonlinear causality expressed through a cubic characteristic polynomial and its discriminant, valid for all allowed parameter ranges. They show that, under these conditions, solutions propagate causally, and that strict inequalities yield sufficient conditions for strong hyperbolicity, ensuring local well-posedness. Importantly, the results do not depend on a particular spacetime metric or equation of state and apply to baryon-rich matter relevant to neutron-star mergers and heavy-ion collisions, providing a mathematically rigorous foundation for future studies of viscous relativistic hydrodynamics in these regimes.
Abstract
We present the first set of fully-nonlinear, necessary and sufficient conditions guaranteeing causal evolution of the initial data for the Israel-Stewart hydrodynamic equations with shear and bulk viscosity coupled to a nonzero baryon current. These constraints not only provide nonlinear causality: they also (a) guarantee the existence of a locally well-posed evolution of the initial data (they enforce strong hyperbolicity) when excluding the endpoints of the bounds, (b) arise from purely algebraic constraints that make no underlying symmetry assumptions on the degrees of freedom and (c) propagate the relevant symmetries of the degrees of freedom over the entire evolution of the problem. Our work enforces a mathematically rigorous foundation for future studies of viscous relativistic hydrodynamics with baryon-rich matter including neutron star mergers and heavy-ion collisions.