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

TL;DR

This paper develops a comprehensive first-order relativistic hydrodynamics model that includes charge currents and ensures hyperbolicity, causality, and stability, advancing the theoretical framework for charged relativistic fluids.

Contribution

It extends the BDNK model to include charge currents with out-of-equilibrium effects, providing a fully second order, hyperbolic, and conservative PDE system with stability analysis.

Findings

Inclusion of out-of-equilibrium charge current is crucial for hyperbolicity.

The model is causal, stable, and entropy-generating across various equations of state.

A new technique for hyperbolicity analysis without explicit first order reduction is introduced.

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. If such correction is not applied, an extra frame restriction must be added to the present in the literature in order to obtain a strongly hyperbolic system.