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Homogeneous Newtonian cosmologies and their perturbations

Published online by Cambridge University Press:  17 February 2009

Peter Szekeres  and
John R. Rankin
John R. Rankin
Affiliation:
Department of Mathematical Physics, University of Adelaide, Adelaide, S.A., 5001, Australia
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Abstract

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A review of Heckmann and Schücking's formulation of Newtonian cosmology is presented, which permits the discussion of models more general than those possessing both homogeneity and isotropy. In particular it is shown that all homogeneous cosmologies may be uniquely specified by the rate of shear tensor as an arbitrary function of time and specifying arbitrary initial values for expansion, rotation and density. Perturbations of these models are now discussed, with a view to their possible implications for galaxy formation. The Jeans criterion is shown to hold in all these models, even in the presence of viscosity; this generalizes a result of Bonnor which only applied to the isotropic case. Furthermore, Bonnor's analysis is considerably simplified in the present paper. Finally, a WKB-type of approximation procedure is described which appears to be successful in estimating the growth rate of unstable fluctuations.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 1 , June 1977 , pp. 114 - 128
Copyright
Copyright © Australian Mathematical Society 1977

References

REFERENCES

[1]Lifschitz, E. M., J. Phys. 10, (1946), 116.Google Scholar
[2]Jeans, J., Astronomy and Cosmology, pp. 345–350, Dover, New York (1961).Google Scholar
[3]Milne, E. A. and McRae, W. H., Quart. J. Math. Oxford Ser. 5 (1934), 64, 73.CrossRefGoogle Scholar
[4]Bondi, H., Cosmology, Cambridge University Press (1958).Google Scholar
[5]Bonnor, W. B., Mon. Not. Roy. Astron. Soc. 117 (1957), 104.Google Scholar
[6]Heckmann, O. and Schücking, E., Handbuch der Physik, Vol. 53, p. 489, Springer-Verlag, Berlin (1959).Google Scholar
[7]Heckmann, O. and Schücking, E., Zeitschrift für Astrophysik 38 (1955), 95.Google Scholar
[8]Layzer, D., Astrophys. J. 59 (1954), 268.Google Scholar
[9]McRae, W. H., Astrophys. J. 60 (1954), 271.Google Scholar
[10]Shepley, L. and Ryan, I., Homogeneous Cosmological Models, Princeton University Press (1974).Google Scholar
[11]Schücking, E., Sonderdruck aus die Nat. 38 (1955), 95.Google Scholar
[12]Ellis, G. F., J. Math. Phys. 8 (1967), 1171.Google Scholar
[13]Hawking, S. W. and Ellis, G. F. R., The Large Scale Structure of Space time, Cambridge University Press (1973).Google Scholar
[14]Lifschitz, E. M. and Khalatnikov, I. M., Adv. in Phys. (Phil. Mag. Suppl.) 12 (1963), 185.Google Scholar
[15]Davidson, W. and Evans, A. B., Int. J. Theor. Phys. 7 (1973), 353.CrossRefGoogle Scholar
[16]Cf. Chandresekhar, S., Hydrodynamics and Hydromagnetic Stability, p. 591, Oxford University Press (1961).Google Scholar