Newtonian universes with shear
Abstract
A special class of Newtonian universes expanding or contracting with shear is analyzed in some detail. It is found that all models have either one or two singular states. Expanding models start from a singularity which is either of 'pancake' or 'needlepoint' character, the latter occurring only in cylindrical models of axial symmetry. A model then either expands indefinitely, or expands to a maximum and returns to a singular state in a finite time. In the general shearing model the singularity is again 'pancake'; in the axisymmetric model the final singularity is 'pancake' if the initial singularity was 'needlepoint', and vice versa. The dominating influence at the singular states is that of shear, not matter. In the ever expanding models there is ultimate isotropy, the shear vanishing. The Newtonian models are compared with relativistic models which are homogeneous with shear
 Publication:

Royal Society Edinburgh Communications Physical Sciences
 Pub Date:
 1977
 Bibcode:
 1977CoRSE..10..123D
 Keywords:

 Astronomical Models;
 Cosmology;
 Isotropic Media;
 Newton Theory;
 Shearing;
 Equations Of Motion;
 Gravitational Fields;
 Nonrelativistic Mechanics;
 Relativity;
 Singularity (Mathematics);
 Time Dependence;
 Astrophysics