A SYMMETRIC HYPERBOLIC FORMULATION OF THE GENERAL RELATIVISTIC MOMENT EQUATIONS FOR MATTER AND RADIATION

Abstract

For a fluid-radiation mixture, i.e. a relativistic gas consisting of material particles and photons, we derive a 14D causal evolution system of first-order symmetric hyperbolic form for a set of basic physical gas-state variables, which is defined relative to a network of observers with arbitrary 4-velocities. This system is obtained by taking moments of the relativistic Boltzmann equation (the so-called central moments) and by truncating and closing the resulting system of moment equations by means of an appropriate (5+9)-moment closure prescription. The material medium under consideration is assumed to be a nonbarotropic perfect gas described by a local Jüttner equilibrium distribution function. With regards to the photon gas, we employ the modified Grad-type approach, which begins by expanding the phase density (i.e. the number density of photons) about a local Planck equilibrium distribution and including the trace-free anisotropic pressure in the expansion. The main advantage of using the above (5+9)-moment closure prescription is that the matter fluid's peculiar velocity and the radiative heat flux are incorporated into the model in a non-perturbative manner, thereby allowing virtually arbitrarily large values for the individual components of these dynamical variables. Within the framework of a reduced 3 + 1 orthonormal frame formalism, we also explain how to choose the initially arbitrary 4-velocity vector field, as this is crucial for the determination of the full 38D causal matter-radiation-gravity system.