Spherically symmetric, self-gravitating dust is always 'self-similar'

Details Spherically symmetric, self-gravitating dust is always 'self-similar' Spherically symmetric, self-gravitating dust is always 'self-similar'

Oct 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989mnras.240..917h&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 240, Oct. 15, 1989, p. 917-929.

Statistics

Computation

15

Cosmic Dust, Einstein Equations, Gravitational Effects, Newtonian Fluids, Computational Astrophysics, Lagrange Coordinates, Partial Differential Equations

Scientific paper

This paper discusses spherically symmetric self-gravitating dust from both the Newtonian and Einsteinian perspectives. A unified treatment in terms of comoving or Lagrangian coordinates is advocated. The most general type of self-similarity can be elucidated with this problem. It is argued that all Tolman solutions are in fact self-similar in the Lie sense, in which an integral exists along a certain curve in space-time. These do not have a simple covariant expression in general at present. The limits in which more restrictive definitions apply are also explored.

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