Statistics – Applications
Scientific paper
Sep 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phdt.........7h&link_type=abstract
Ph.D. Thesis Texas Univ., Austin.
Statistics
Applications
3
Computerized Simulation, Cosmology, Mathematical Models, Relativity, Space-Time Functions, Symmetry, Universe, Applications Programs (Computers), Asymptotic Properties, Gravitational Waves, Hamiltonian Functions, Inhomogeneity
Scientific paper
Two computer codes whose purpose is the study of inhomogeneous cosmological models are described. The first code assumes spherical symmetry, whereas the second is more general assuming only axisymmetry. Both codes are based upon the 3+1 decomposition of Arnowitt, Deser, and Misner. With this approach, general relativity is cast into a dynamical form which has proved fruitful for numerical solution. The conformal approach of York is employed to solve the initial-value problem. Gauge conditions are set in order to write the three-metric in the simplest possible form. Constant-mean-curvature time slicing is used to determine the foliation of spacelike hypersurfaces. In the case of spherical symmetry, the three-metric is put into diagonal form. A fully-constrained evolution is performed. The code has full hydrodynamical capabilities. Outer boundary conditions are applied by requiring that the metric become the Friedmann-Robertson-Walker metric appropriate to the matter energy density at the edge of the computational mesh. The code tests carried out are discussed. The axisymmetric code is based upon a code developed by Wilson and Dykema and by Evans to treat the problem of nonspherical gravitational collapse in asymptotically-flat spacetimes. Appropriate modifications were made to permit cosmological models to be studied. The three-metric is put into quasi-isotropic form, leaving two metric variables for which we must solve. One, the conformal factor, is determined by the Hamiltonian constraint. The other represents the single dynamical degree of freedom allowed by our symmetries. A partially-constrained evolution is employed in which only the Hamiltonian constraint is enforced on each time slice.
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