
Contents
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80. Role of the Relativistic Theory 80. Role of the Relativistic Theory
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81. Time-Orthogonal Coordinates 81. Time-Orthogonal Coordinates
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82. The Field Equations for hαβ 82. The Field Equations for hαβ
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83. Gravitational Waves 83. Gravitational Waves
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84. Newtonian Approximation 84. Newtonian Approximation
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85. Linear Perturbation Equations for the Matter 85. Linear Perturbation Equations for the Matter
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86. Behavior of Density Perturbations at Wavelength ≫ ct 86. Behavior of Density Perturbations at Wavelength ≫ ct
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87. Spherical Model 87. Spherical Model
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88. Evolution of Acoustic Waves 88. Evolution of Acoustic Waves
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89. Nonlinear Acoustic Waves 89. Nonlinear Acoustic Waves
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A. Relativistic simple waves A. Relativistic simple waves
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B. Second order perturbation theory B. Second order perturbation theory
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90. Incompressible Flow 90. Incompressible Flow
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91. Behavior of Collisionless Particles 91. Behavior of Collisionless Particles
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92. Linear Dissipation or Adiabatic Perturbations 92. Linear Dissipation or Adiabatic Perturbations
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A. Description of the matter and radiation A. Description of the matter and radiation
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B. Limit tc → 0 B. Limit tc → 0
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C. Damping by photon diffusion C. Damping by photon diffusion
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D. Linear transfer function for adiabatic perturbations: characteristic masses D. Linear transfer function for adiabatic perturbations: characteristic masses
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93. Residual Fluctuations in the Microwave Background 93. Residual Fluctuations in the Microwave Background
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A. Small angular scales A. Small angular scales
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B. Large angular scales B. Large angular scales
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94. Isothermal Perturbations 94. Isothermal Perturbations
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A. Origin A. Origin
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B. Behavior B. Behavior
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V. Relativistic Theory of the Behavior of Irregularities in an Expanding World Model
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Published:September 2020
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Abstract
This chapter presents the full relativistic analysis of the evolution of mass clustering. The full relativistic theory is needed to deal with three important aspects of density irregularities in the early universe. First, when the pressure is high the relativistic active gravitational mass and inertial mass associated with pressure affect the dynamics. Second, when the mean density is high, a fluctuation of even modest fractional amount containing a modest mass can have a large effect on the space curvature. One is thus led to deal with the interaction of speculations on the nature of the mass distribution and of the geometry in the early universe. Third, the horizon shrinks to zero at the time of the big bang: the seed fluctuations out of which galaxies might form were larger than the horizon and so were not in causal connection reckoned from the time of the big bang. Of course, this curious point applies as well to the homogeneous background: it was somehow contrived that all parts of the universe now visible were set expanding with quite precise uniformity even though an observer could not have discovered this much before the present epoch.
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