A hyperbolic theory of relativistic conformal dissipative fluids

TL;DR

This paper develops a comprehensive hyperbolic framework for relativistic conformal dissipative fluids, providing a unified description, constitutive relations, and conditions for well-posed initial value problems.

Contribution

It introduces a master scalar function characterizing the entire family of conformal fluids, enabling explicit derivation of constitutive relations and hyperbolicity conditions.

Findings

Identification of equilibrium states and heat flux laws.

Explicit form of the master scalar function up to second order.

Existence of symmetric hyperbolic theories near equilibrium.

Abstract

We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of evolution variables whose dynamics is governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory, as well as to derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories-- and near equilibrium configurations-- there exist symmetric hyperbolic ones, implying that for them one can define well posed initial value problems.