Post-Newtonian Equations of Motion in the Flat Universe : Astrophysics and Relativity
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概要
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Using the (3+1) formalism, we derive the post-Newtonian (PN) equations of motion in a flat universe. To derive the equations of motion, we must carefully consider two points, one being the choice of the density in the Newtonian order (ρ_N) and the other the choice of the gauge condition. In choosing ρ_N, we require that the density fluctuation ρ_N - ρ_o agrees with a gauge invariant quantity in the linear approximation theory. As a gauge condition, we propose the cosmological post-Newtonian (CPN) slice condition with the pseudo transverse-traceless gauge condition, by which the evolution of the geometric variables derived in the PN approximation in the early stage of universe agrees with that of the gauge invariant quantities in the linear approximation. In the derived equations of motion, the force is calculated from six potentials which satisfy the Poisson equations. Hence, our formalism can be easily applied to numerical simulations in which the standard technique (e.g., particle-mesh method) is used. We apply the PN formula to the one-dimensional (1D) Zel'dovich solution to demonstrate that our strategy works well, and also to determine the effect of the PN forces on the evolution of the large-scale structure. It is found that the behavior of the density fluctuation and metric quantities in the early stage obtained by the present formalism agrees with that of the gauge invariant quantities in the linear approximation, although they do not always agree within the previous formalism due to the appearance of spurious gauge modes. We also discuss the evolution of the non-linear density fluctuation with very large scale, which may be affected by the PN correction in the last stage of the evolution.
- 理論物理学刊行会の論文
- 1995-07-25
著者
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Sakka Makiko
Graduate School Of Bioresources Mie Univ.
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Shibata M
Univ. Tokyo Tokyo Jpn
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Asada Hideki
Kobe University
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Shibata Masaru
Department Of Agricultural Chemistry Kyoto University:(present)asahi Kasei Chemicals Industry Co. Lt
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ASADA Hideki
Yukawa Institute for Theoretical Physics, Kyoto University
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ASADA Hideki
Department of Earth and Space Science, Faculty of Science Osaka University
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Asada Hideki
Department Of Earth And Space Science Faculty Of Science Osaka University
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SHIBATA Masaru
Department of Earth and Space Science Faculty of Science, Osaka University
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ASADA Hideki
Faculty of Science and Technology, Hirosaki University:Max-Planck-Institut fur Astrophysik
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ASADA Hideki
Department of Earth and Space Science Faculty of Science, Osaka University
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ASADA Hideki
Faculty of Science and Technology, Hirosaki University:Max-Planck-Institute fur Gravitationsphysik
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Asada Hideki
Department of Applied Chemistry, Faculty of Engineering, Osaka University
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