Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909820668346368 |
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| author | Cordeiro, Ian Bemfica, Fábio S. Speranza, Enrico Noronha, Jorge |
| author_facet | Cordeiro, Ian Bemfica, Fábio S. Speranza, Enrico Noronha, Jorge |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_01512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics Cordeiro, Ian Bemfica, Fábio S. Speranza, Enrico Noronha, Jorge Nuclear Theory High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology 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. |
| title | Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics |
| topic | Nuclear Theory High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.01512 |