Mathematics – Logic
Scientific paper
Sep 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6.1253b&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, Sept. 1989, p. 1253-1265.
Mathematics
Logic
25
Astronomical Models, Newton Theory, Relativity, Universe, Asymptotic Properties, Big Bang Cosmology, Many Body Problem, One Dimensional Flow, Three Dimensional Flow
Scientific paper
A detailed analysis is made of the status of the no-hair conjectures of general relativistic inflationary universes in Newtonian cosmological models. It is shown that the no-hair theorem cannot be proved in Newtonian gravity with a positive cosmological constant. Rigorous results can be derived to show that the mean volume of the universe approaches the behavior of the Newtonian de Sitter universe at large times but no information is available about its shape. This manifestation of the 'gravitational paradox' is displayed both in the fluid and N-body formulations of Newtonian cosmology. New asymptotic results are proven for the asymptotic behavior of self-gravitating fluids and for the N-body problem when the cosmological constant is nonzero. New exact solutions for one- and three-dimensional fluid flows with nonzero cosmological constant are given. These solutions are shown to be stable attractors for the Newtonian cosmological problem. They are generalizations of the exact Zel'dovich 'pancake' solutions to the case of nonzero cosmological constant.
Barrow John D.
Goetz Guenter
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