Computer simulation of timedependent spherically symmetric spacetimes containing radiating fluids: Formalism and code tests
Abstract
General equations are presented for general relativistic radiation hydrodynamics. The 3 + 1 Einstein equations including a radiation component in the energymomentum tensor are derived and these equations are specialized to spherical symmetric spacetimes and the isotropic gauge. The 3 + 1 equations are derived for general relativistic hydrodynamics, including the radiation 4force density, and the 3 + 1 general relativistic Boltzmann equation, all for spherical symmetric spacetimes. These equations are then specialized to the isotropic gauge. The implicit finite differencing of the Boltzmann equation and of the radiation contribution to the hydrodynamics equations are described. A new implicit numerical scheme is presented for the matterradiation coupling, that is, for the collision term in the Boltzmann equation and the radiation 4force density in the hydrodynamics equations. This scheme allows analytic matrix inversion of the finite difference equations for these terms and does not rely on partial temperatures. Evans' hydrodynamics code for spherically symmetric spacetimes, which is used in conjunction with the radiation code is described. The results of a code test for the radiation transport and matterradiation coupling that serves as a benchmark for the code is presented. Finally, the results of a general relativistic example and code tests which was developed is described. A star was constructed in general relativistic hydrodynamic and thermodynamic equilibrium by solving the OppenheimerVolkoff equations coupled to the equations for thermodynamic equilibrium. The methods used to numerically integrate this system of ordinary differential equations are discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1988
 Bibcode:
 1988PhDT........21M
 Keywords:

 Collisions;
 Computerized Simulation;
 Finite Difference Theory;
 Fluids;
 Hydrodynamics;
 Radiation Transport;
 SpaceTime Functions;
 Thermodynamic Equilibrium;
 Time Dependence;
 Difference Equations;
 Differential Equations;
 Einstein Equations;
 Formalism;
 Isotropy;
 Matrices (Mathematics);
 Measuring Instruments;
 Tensors;
 Astrophysics