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arXiv · 2602.20254

A strongly hyperbolic viscous relativistic hydrodynamics theory with first-order charge current

Federico Schianchi·Fernando Abalos
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Abstract

We extend the first order dissipative relativistic hydrodynamics model of Bemfica-Disconzi-Noronha- Kovtun (BDNK) in order to include the charge number current in full first order expansion with out-of-equilibrium contribution proportional to the evolution equation of the ideal fluid. We obtain a fully second order system of partial differential equation (PDE) that can be casted in a fully conservative way. We analyze the hyperbolicity of this model coupled to Einstein field equations using a newly developed technique that allows for hyperbolicity studies without explicit first order reduction. Furthermore, we identify a frame choice where our formulation is causal, stable and with positive entropy generation for a wide range of equations of state (EoS). Our analysis shows that the inclusion of an out-of-equilibrium correction to the charge current, plays an important role in guaranteeing the strong hyperbolicity and, therefore, the well-posedness of the system.

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Federico Schianchi, Fernando Abalos. 2026-02-23. A strongly hyperbolic viscous relativistic hydrodynamics theory with first-order charge current. https://arxiv.org/abs/2602.20254

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