Numerical solutions of high-frequency perturbations in Bianchi type IX models

Details Numerical solutions of high-frequency perturbations in Bianchi type IX models Numerical solutions of high-frequency perturbations in Bianchi type IX models

May 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983apj...268..513s&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 268, May 15, 1983, p. 513-526.

Computer Science

Numerical Analysis

5

Astronomical Models, Cosmology, Numerical Analysis, Perturbation Theory, Relativity, Einstein Equations, Galactic Evolution, Gravitational Waves, Metric Space

Scientific paper

The problem in perturbation theory in general relativity is finding a natural gauge which simplifies the equations considerably. The first and second order perturbation equations in the 'Lorentz gauge' were solved using the two-timing method. The equations were deduced from the equations of Einstein in the presence of a matter energy-momentum tensor of a perfect fluid with equation of state p = (gamma - 1)rho. It is found that the 0-0 component of the first order equations together with the gauge conditions are consistent with the Bianchi type V model, without axial symmetry. It represents a 'ground state' situation of the Bianchi type IX model (Mixmaster model). The second order equations, describing the reaction back of the gravitational waves on the slowly varying background, give rise to rotation and will disturb the isotropization mechanism. The numerical solutions show all the features which are expected to appear. Moreover, it is found that the frequency of the perturbations increases with gamma.

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