Kuwait Journal of Science

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Volume :31 Issue : 2 2004      Add To Cart                                                                    Download

Nonlinear gravitational perturbation analysis including a cosmological term


*Physics Department, Campus Drie Eiken, University of An twerp, B-26]0 Antwerp,

e-mail: Dirk.Callebaut@ua.ac.be and ** Institute for Environmental Electromagnetics, 3-8-18, Komagome, Toshima-ku, Tokyo 170, Japan


An improved nonlinear analysis developed by us is applied here to an infinite homogeneous gravitating medium at rest, using a cosmological constant A in the Newtonian approximation. Several higher order terms are calculated using mathematica. Three different ways have been explored to handle the equations and to find out which one is best suited.

The stability criterion of Jeans is confirmed in the limit when A approaches zero. This is quite satisfying as Jeans had derived his criterion from an inconsistent equilibrium and because the stability criterion is used not only for the universe but for stars and galaxies as well. The higher order terms allow corrections to the linearized theory; moreover using analytical extensions or graphical methods we are able to make statements on the convergence of the Fourier series. As we have used the polytropic law for the relation between pressure and density (p = Kp
G) with an arbitrary polytropic exponent G the results are applicable equally well to the adiabatic case as to the isothermal one (when radiation should fiat out the temperature differences) or any intermediate or alternative one.

Keywords: Cosmology; Fourier analysis; perturbation theory; waves and wave propagation.

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