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Prog. Theor. Phys. Vol. 37 No. 1 (1967) pp. 60-74

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On the Gravitational Instability in an Expanding Universe

— Reformulation of Lifshitz's Theory —

Hidekazu Nariai, Kenji Tomita and Shoji Kato*

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima-ken
*Department of Astronomy, University of Tokyo, Tokyo

(Received August 25, 1966)

Abstract:

In view of a new interest motivated by the discovery of a cosmic black-body radiation for the problem of galgxay formation in an evolving universe, an attempt is made to reformulate Lifshitz's relativistic theory of the gravitational instability in such a way that the rewritten formalism permits us to make a full comparison with Bonnor's approach based on the Newtonian cosmology. The essence of our reformulation lies in deriving a differential equation for the density contrast δε/ε which is a 4-scalar independent of Lifshit's coordinate conditions. The differential equation is solved, except for such a time interval that non-adiabatic processes are effective. At the later stage, our equation is the same as Bonnor's, but this does not necessarily mean that both approaches equivalent to each other at the stage. The latter situation is illustrated by considering a mass concentration in a spherical region, which depends not only on the density contrast, but also on the metric perturbation.


URL : http://ptp.ipap.jp/link?PTP/37/60/
DOI : 10.1143/PTP.37.60

[ Full Text PDF : FREE ACCESS (835K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 37 No. 5 (1967) pp. 831-846 :
    Non-Linear Theory of Gravitational Instability in the Expanding Universe
    Kenji Tomita
  2. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 686-694 :
    The Lagrangian Approach to the Gravitational Instability in an Expanding Universe
    Hidekazu Nariai
  3. Progress of Theoretical Physics Vol. 41 No. 5 (1969) pp. 1379-1381 :
    The Gravitational Instability in the Lemaître Universe
    Hidekazu Nariai
  4. Progress of Theoretical Physics Vol. 42 No. 1 (1969) pp. 9-23 :
    Formation of Gravitationally Bound Primordial Gas Clouds
    Kenji Tomita
  5. Progress of Theoretical Physics Vol. 42 No. 3 (1969) pp. 544-554 :
    Gravitational Instability in the Brans-Dicke Cosmology
    Hidekazu Nariai
  6. Progress of Theoretical Physics Vol. 45 No. 2 (1971) pp. 370-385 :
    Mass of a Galaxy and Dissipative Process in the Hot Universe
    Humitaka Satō
  7. Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 118-133 :
    Newtonian Hydrodynamics in an Expanding Universe in Terms of the Scalar-Tensor Theory
    Hidekazu Nariai
  8. Progress of Theoretical Physics Vol. 47 No. 2 (1972) pp. 416-443 :
    Non-Linear Theory of Gravitational Instability in the Expanding Universe. III
    Kenji Tomita
  9. Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1150-1169 :
    On Inhomogeneous Cosmological Models Containing Space-Like and Time-Like Singularities Alternately
    Kenji Tomita
  10. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 1860-1869 :
    On Local Behaviour of Congruences in Self-Gravitating Viscous, Compressible, Thermally Conducting Fluid with Infinite Electrical Conductivity and Constant Magnetic Permeability
    G. G. Asgekar and T. H. Date
  11. Progress of Theoretical Physics Vol. 67 No. 4 (1982) pp. 1076-1092 :
    Primordial Irregularities in an Early Universe with Vacuum Phase Transitions
    Kenji Tomita
  12. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 674-682 :
    Generation and Evolution of the Density Fluctuation in the Evolving Universe. II
    Hideo Kodama
  13. Progress of Theoretical Physics Supplement No.78 (1984) pp. 1-166 :
    Cosmological Perturbation Theory
    Hideo Kodama and Misao Sasaki

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