Astronomy and Astrophysics – Astronomy
Scientific paper
May 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991mnras.250...69p&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 250, May 1, 1991, p. 69-74.
Astronomy and Astrophysics
Astronomy
13
Einstein Equations, Interstellar Matter, Relativistic Theory, Similarity Theorem, Space-Time Functions, Spatial Distribution, Big Bang Cosmology, Energy Distribution, Mass Distribution, Symmetry
Scientific paper
The conditions under which relativistic spherical distribution of dust possesses self-similar symmetry are studied. It is found that there are homothetic, partially homothetic, and conformal solutions depending on how the mass and energy are distributed through the matter. It is shown that the properties of such solutions are quite different from the properties of self-similar Newtonian dust. In particular, the 'big bang' hypersurface is entirely determined by the symmetry in the relativistic case, while it is entirely free in the Newtonian case. The similarity variable is determined uniquely by a simple differential equation. In all cases the space has similarity in the usual geometrical sense. The solutions are regular everywhere, except the hyperbolic and elliptic homothetic solutions which are singular at the center of symmetry. The results are used to gain insight into the nature of self-similarity. The generality of the results is discussed.
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