A class of solutions for self-gravitating dust in Newtonian gravity

Details A class of solutions for self-gravitating dust in Newtonian gravity A class of solutions for self-gravitating dust in Newtonian gravity

Nov 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987jmp....28.2714b&link_type=abstract

Journal of Mathematical Physics, Volume 28, Issue 11, November 1987, pp.2714-2719

Mathematics

Mathematical Physics

26

Scientific paper

The Lagrange method is used to obtain a class of solutions to the three-dimensional hydrodynamical equations governing the motion of matter with vanishing pressure in its own Newtonian gravitational field. The class is characterized by the property that each fluid particle has constant acceleration. The class contains rotational and irrotational flows. For rotational flows the expansion tensor has one zero eigenvalue, while for irrotational flows it has two zero eigenvalues, which implies that every fluid element contracts or expands in two or one spatial directions, respectively; nevertheless, the density depends on all three coordinates. The general one-dimensional solution is included as a subclass.

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