A new continuum model for general relativistic viscous heat-conducting media

TL;DR

This paper introduces a relativistic continuum model for viscous heat-conducting media that respects causality and the structure of General Relativity, using a hyperbolic system with relaxation terms to describe irreversible processes.

Contribution

It proposes a novel, non-equilibrium based continuum model compatible with relativity, deriving classical transport coefficients as effective parameters.

Findings

The model is formulated as a hyperbolic system with relaxation terms.

Classical viscosity and heat conductivity are recovered asymptotically.

Numerical examples demonstrate the model's viability.

Abstract

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein's Special Relativity and the Euler-Lagrange structure of General Relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as the viscosity and heat conductivity are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach.