Self-similar perturbations of a Kantowski-Sachs model

Details Self-similar perturbations of a Kantowski-Sachs model Self-similar perturbations of a Kantowski-Sachs model

Mar 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...405...34c&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 405, no. 1, p. 34-50.

Astronomy and Astrophysics

Astrophysics

6

Astronomical Models, Cosmology, Perturbation, Universe, Asymptotic Methods, Einstein Equations

Scientific paper

A new family of spherically symmetric similarity solutions which represent inhomogeneous perturbations of the Kantowski-Sachs model is discussed. The present solutions are more general than the similarity solutions found by Wesson (1986) and Ponce de Leon (1988), in that the azimuthal as well as the radial metric component is allowed to depend on the similarity variable. It is demonstrated that for each alpha there is a one-parameter family of spherically symmetric solutions which are asymptotic to the Kantowski-Sachs model at large or small distances. For positive pressure (alpha is greater than 0) some of the solutions pass through a sonic point, and all of these have an infinite pressure gradient there. In the alpha is less than 0 case there is no sonic point. The alpha = 1/3 and alpha = 1/2 solutions are examined numerically.

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