Title
Nonlinear gravitational perturbation analysis including a cosmological term Nonlinear gravitational perturbation analysis including a cosmological term
Author
Publication type
article
Publication
Subject
Engineering sciences. Technology
Source (journal)
KUWAIT JOURNAL OF SCIENCE AND ENGINEERING
Volume/pages
31(2004) :2 , p. 33-45
ISSN
1024-8684
ISI
000231930700003
Carrier
E
Target language
English (eng)
Abstract
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 = K rho(Gamma)) with an arbitrary polytropic exponent F the results are applicable equally well to the adiabatic case as to the isothermal one (when radiation should flat out the temperature differences) or any intermediate or alternative one.
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