Nonlinear Causality and Strong Hyperbolicity of Einstein-Israel-Stewart Theories of Transient Relativistic Fluid Dynamics

arXiv:2607.05639 · nucl-th, astro-ph.HE, gr-qc · Submitted 2026-07-06 · Read on arXiv

Ian Cordeiro, Enrico Speranza, Fábio S. Bemfica, Marcelo M. Disconzi, Jorge Noronha

nucl-th, astro-ph.HE, gr-qc

Submitted: 2026-07-06

Comments: 44 pages, 1 figure

Code: https://github.com/itc2-github/Nonlinear-Causality-and-Strong-Hyperbolicity-of-Einstein-IS-Theoriesfrom-DNMR

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Initial Data — 31× in this paper · explained in 2 episodes
• Bulk Viscosity — 10× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Accretion Flows — 2× in this paper · explained in 1 episode
• Boltzmann Equation — 2× in this paper · explained in 2 episodes
• Conservation Laws — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Physical Constraints — 2× in this paper · explained in 7 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

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• Hydrodynamic Modeling of Heavy-Ion Collisions
• Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Multi-messenger Observations of a Binary Neutron Star Merger
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Applying the Gibbs stability criterion to relativistic hydrodynamics
• Thermodynamic stability implies causality
• Can we make sense of dissipation without causality?
• Theories of Relativistic Dissipative Fluid Dynamics
• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• First-order relativistic hydrodynamics is stable
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Stable and causal relativistic Navier-Stokes equations
• Causal and stable first-order chiral hydrodynamics
• Lectures on hydrodynamic fluctuations in relativistic theories
• Local well-posedness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics
• Strongly hyperbolic quasilinear systems revisited, with applications to relativistic fluid dynamics
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Relativistic viscous hydrodynamics, conformal invariance, and holography

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