Cosmological Relativity: The Special and General Theories for the Structure of the Universe

Overview

The theory presented in this book is a combination of Einstein's original special and general relativity, but now the starting point is not the propagation of light but the expansion of the Universe. The traditional Hubble constant H[subscript 0] (which is not constant) is called in this book the Hubble parameter. Its value at low gravity is denoted by h, and its reciprocal is denoted by [tau]. Thus [tau] is the Big Bang time (some authors call it the Hubble-Carmeli constant). This is actually the only constant ...
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Overview

The theory presented in this book is a combination of Einstein's original special and general relativity, but now the starting point is not the propagation of light but the expansion of the Universe. The traditional Hubble constant H[subscript 0] (which is not constant) is called in this book the Hubble parameter. Its value at low gravity is denoted by h, and its reciprocal is denoted by [tau]. Thus [tau] is the Big Bang time (some authors call it the Hubble-Carmeli constant). This is actually the only constant that appears in this theory, just as c is the only constant that appears in Einstein's theory. There is no cosmological constant but there is a critical mass density. The theory presents general relativity in the space-velocity (of the receding galaxies) which is later on extended to include the time dimension. So far all experimental findings are satisfied by this theory.

About the Author:
Moshe Carmeli is Albert Einstein Emeritus Professor of Theoretical Physics at Ben Gurion University in Israel

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Product Details

  • ISBN-13: 9789812700759
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 10/28/2006
  • Pages: 152
  • Product dimensions: 6.20 (w) x 9.10 (h) x 0.60 (d)

Table of Contents


Preface     V
Introduction     1
Remarks on cosmological special relativity     1
Cosmological Special Relativity     3
The Galileo transformation and its generalization     3
The Galileo transformation     3
Difficulties with light     5
Role of velocity in classical physics     5
Nonrelativistic cosmological transformation     6
Nonrelativistic transformation     6
Difficulties at the Big Bang     6
Extension to the Lorentz transformation     8
Invariance of light propagation     8
The Lorentz transformation     8
Extension to the cosmological transformation     9
Invariance of the Big Bang time     9
The cosmological transformation     9
Temperature of the Universe     10
Conclusions     11
Line elements in Einstein's special relativity and in cosmological special relativity     11
Line element in Einstein's relativity     11
Light propagation     12
Line element in cosmological special relativity     12
Hubble's expansion     12
Inflation of the Universe     15
Matter density     15
Ratio of volumes     16
Minimal acceleration in Nature     16
Relation to Pioneer spacecrafts     17
Redshift and cosmic time     17
Field equations of a different kind     19
Examples     21
Cosmological special relativity in five dimensions     22
Subtransformations     23
Electrodynamics in five dimensions     24
Field equations     25
Generalized Maxwell's equations     25
The mix-up     26
Does the Cabibbo angle describe a rotation in the time-velocity plane?     28
Elements of General Relativity     29
Riemannian geometry     29
Transformation of coordinates     29
Contravariant vectors     30
Invariants. Covariant vectors     31
Tensors     32
Metric tensor     32
Christoffel symbols     33
Covariant differentiation     34
Riemann, Ricci and Einstein tensors     36
Geodesics     37
Bianchi identities     38
Principle of equivalence     39
Null experiments. Eotvos experiment     39
Principle of general covariance      41
Gravitational field equations     42
Einstein's field equations     43
Deduction of Einstein's equations from variational principle     44
The electromagnetic energy-momentum tensor     45
The Schwarzschild metric     46
Experimental tests of general relativity     51
Gravitational red shift     51
Effects on planetary motion     52
Deflection of light     56
Gravitational radiation experiments     59
Radar experiment     59
Low-temperature experiments     60
Equations of motion     61
Geodesic postulate     61
Equations of motion as a consequence of field equations     61
Self-action terms     63
Einstein-Infeld-Hoffmann method     67
Newtonian equation of motion     69
Einstein-Infeld-Hoffmann equation     70
Decomposition of the Riemann tensor     71
Cosmological General Relativity     73
Introduction     73
Space and velocity     74
Gravitational field equations     74
Universe expansion     75
Energy-momentum tensor     75
Independent field equations      76
Solution of the field equations     76
Simple solution     76
Pressure     77
Line element     77
Physical meaning     77
[Omega subscript m] > 1     78
[Omega subscript m] < 1     78
[Omega subscript m] = 1     78
The accelerating Universe     78
Tri-phase expansion     79
Theory versus experiment     80
Value of the Big Bang time [tau]     80
Value of [Characters not reproducible]     82
Comparison with general relativity     84
Recent developments on dark matter     84
Cosmological General Relativity in Five Dimensions     87
Introduction     87
Five-dimensional manifold of space, time and velocity     87
Universe with gravitation     88
The Bianchi identities     89
The gravitational field equations     89
Velocity as an independent coordinate     90
Effective mass density in cosmology     90
The accelerating Universe     91
Preliminaries     91
Expanding Universe     93
Decelerating, constant and accelerating expansions      95
Accelerating Universe     96
The Tully-Fisher formula: Nonexistence of halo dark matter     97
The Geodesic Equation     98
Equations of motion     99
The Tully-Fisher law     102
Cosmological redshift analysis     104
The redshift formula     104
Particular cases     105
Conclusions     106
Verification of the classical general relativity tests     106
Comparison with general relativity     106
Gravitational redshift     109
Motion in a centrally symmetric gravitational field     111
Deflection of light in a gravitational field     117
Gravitational waves     120
Mathematical Conventions     123
Components of the Ricci tensor     124
Integration of the Universe Expansion Equation     127
Index     129
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