On the general relativistic symmetric hyperbolic moment system for matter and radiation: local rotational symmetry

Details On the general relativistic symmetric hyperbolic moment system for matter and radiation: local rotational symmetry On the general relativistic symmetric hyperbolic moment system for matter and radiation: local rotational symmetry

Aug 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cqgra..24.4079b&link_type=abstract

Classical and Quantum Gravity, Volume 24, Issue 16, pp. 4079-4106 (2007).

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For the one-dimensional, locally rotationally symmetric case, we employ the relativistic Boltzmann equations and the moment methods to derive a 6D causal evolution system of first-order symmetric hyperbolic form for a fluid-radiation mixture, i.e., a relativistic gas composed of material particles and photons. The material medium is assumed to be a nonbarotropic perfect gas and the evolution equations for this medium are obtained by using the local Jüttner equilibrium distribution function as seen by an observer with arbitrary 4-velocity. In order to derive the evolution equations for the photon gas, we develop the modified Grad-type method which consists of expanding the phase density (i.e., the number density of photons) about a local Planck equilibrium distribution function and including the trace-free anisotropic pressure in the expansion. In our approach, it is significant that the matter fluid's peculiar velocity and the radiative heat flux (relative to an arbitrary 4-velocity vector field) are incorporated into the model in a non-perturbative manner, thereby allowing arbitrarily large values for the two nonvanishing components of these dynamical variables. The additional difference about the treatment here as opposed to other treatments is that we do not neglect terms in the evolution equations which involve small first-order quantities multiplying the spatial frame derivatives of hydrodynamical variables.

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