Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations
J. Félix Salazar, Ana Laura García-Perciante, Olivier Sarbach
TL;DR
The paper develops a fully nonlinear, relativistic dissipative fluid theory in the trace-fixed particle (TFP) frame, ensuring causality and stability by proving strong hyperbolicity of a first-order quasilinear reformulation. By introducing auxiliary gradient fields and constraints, the authors construct a constrained system whose principal symbol decomposes into scalar, vector, and tensor blocks and admits smooth, state-dependent symmetrizers. They explicitly diagonalize the blocks under a key set of conditions, derive a consistent constraint propagation system, and prove local well-posedness of the Cauchy problem for the nonlinear system. The framework preserves thermodynamic consistency, aligns with the second law, and provides a tractable, well-posed model suitable for numerical relativity and high-energy astrophysical contexts.
Abstract
In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium states, here we prove that the full nonlinear system of equations can be cast into a first-order quasilinear system which is strongly hyperbolic. By rewriting the system in first-order form, auxiliary constraints are introduced. However, we show that these constraints propagate, and thus our theory leads to a well-posed Cauchy problem.