Physics
Scientific paper
Mar 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........19f&link_type=abstract
Thesis (PH.D.)--PRINCETON UNIVERSITY, 1982.Source: Dissertation Abstracts International, Volume: 43-05, Section: B, page: 1523.
Physics
Scientific paper
Perturbations to a homogeneous and isotropic background mass distribution have previously been studied in the context of the big bang model in attempts to reproduce the large scale clustering of matter observed today. The work has focused on the results of linear perturbation theory, it being tacitly assumed that the perturbations are so small that they do not cause significant space curvature, and hence are in no danger of undergoing gravitational collapse. I study the evolution of spherically symmetric mass density fluctuations large enough to cause significant space curvature, and which have spatial extents that initially exceed the horizon size. The spherical symmetry permits Einstein's field equations to be reduced to a system of four coupled nonlinear partial differential equations, which I integrate numerically. To stabilize the numerical integration smoothing procedures in both the temporal and spatial directions are introduced. I conclude that if the amplitude (at the origin) of a spherically symmetric mass density fluctuation in the early, radiation dominated universe exceeds 0.17 of the background density before it enters the horizon, it will undergo gravitational collapse. Within the constraints provided by the background model, this large density fluctuation evolves into an object with a mass (GREATERTHEQ) 10('16) solar masses, and with a spatial extent (GREATERTHEQ) 40 Megaparsecs.
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