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

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  • Format: Hardcover
  • Copyright: 2006-10-30
  • Publisher: World Scientific Pub Co Inc
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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 H0 (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 t. Thus t 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 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.

Author Biography

Moshe Carmeli is Albert Einstein Emeritus Professor of Theoretical Physics at Ben Gurion University in Israel.

Table of Contents

Prefacep. V
Introductionp. 1
Remarks on cosmological special relativityp. 1
Cosmological Special Relativityp. 3
The Galileo transformation and its generalizationp. 3
The Galileo transformationp. 3
Difficulties with lightp. 5
Role of velocity in classical physicsp. 5
Nonrelativistic cosmological transformationp. 6
Nonrelativistic transformationp. 6
Difficulties at the Big Bangp. 6
Extension to the Lorentz transformationp. 8
Invariance of light propagationp. 8
The Lorentz transformationp. 8
Extension to the cosmological transformationp. 9
Invariance of the Big Bang timep. 9
The cosmological transformationp. 9
Temperature of the Universep. 10
Conclusionsp. 11
Line elements in Einstein's special relativity and in cosmological special relativityp. 11
Line element in Einstein's relativityp. 11
Light propagationp. 12
Line element in cosmological special relativityp. 12
Hubble's expansionp. 12
Inflation of the Universep. 15
Matter densityp. 15
Ratio of volumesp. 16
Minimal acceleration in Naturep. 16
Relation to Pioneer spacecraftsp. 17
Redshift and cosmic timep. 17
Field equations of a different kindp. 19
Examplesp. 21
Cosmological special relativity in five dimensionsp. 22
Subtransformationsp. 23
Electrodynamics in five dimensionsp. 24
Field equationsp. 25
Generalized Maxwell's equationsp. 25
The mix-upp. 26
Does the Cabibbo angle describe a rotation in the time-velocity plane?p. 28
Elements of General Relativityp. 29
Riemannian geometryp. 29
Transformation of coordinatesp. 29
Contravariant vectorsp. 30
Invariants. Covariant vectorsp. 31
Tensorsp. 32
Metric tensorp. 32
Christoffel symbolsp. 33
Covariant differentiationp. 34
Riemann, Ricci and Einstein tensorsp. 36
Geodesicsp. 37
Bianchi identitiesp. 38
Principle of equivalencep. 39
Null experiments. Eotvos experimentp. 39
Principle of general covariancep. 41
Gravitational field equationsp. 42
Einstein's field equationsp. 43
Deduction of Einstein's equations from variational principlep. 44
The electromagnetic energy-momentum tensorp. 45
The Schwarzschild metricp. 46
Experimental tests of general relativityp. 51
Gravitational red shiftp. 51
Effects on planetary motionp. 52
Deflection of lightp. 56
Gravitational radiation experimentsp. 59
Radar experimentp. 59
Low-temperature experimentsp. 60
Equations of motionp. 61
Geodesic postulatep. 61
Equations of motion as a consequence of field equationsp. 61
Self-action termsp. 63
Einstein-Infeld-Hoffmann methodp. 67
Newtonian equation of motionp. 69
Einstein-Infeld-Hoffmann equationp. 70
Decomposition of the Riemann tensorp. 71
Cosmological General Relativityp. 73
Introductionp. 73
Space and velocityp. 74
Gravitational field equationsp. 74
Universe expansionp. 75
Energy-momentum tensorp. 75
Independent field equationsp. 76
Solution of the field equationsp. 76
Simple solutionp. 76
Pressurep. 77
Line elementp. 77
Physical meaningp. 77
[Omega subscript m] > 1p. 78
[Omega subscript m] < 1p. 78
[Omega subscript m] = 1p. 78
The accelerating Universep. 78
Tri-phase expansionp. 79
Theory versus experimentp. 80
Value of the Big Bang time [tau]p. 80
Value of [Characters not reproducible]p. 82
Comparison with general relativityp. 84
Recent developments on dark matterp. 84
Cosmological General Relativity in Five Dimensionsp. 87
Introductionp. 87
Five-dimensional manifold of space, time and velocityp. 87
Universe with gravitationp. 88
The Bianchi identitiesp. 89
The gravitational field equationsp. 89
Velocity as an independent coordinatep. 90
Effective mass density in cosmologyp. 90
The accelerating Universep. 91
Preliminariesp. 91
Expanding Universep. 93
Decelerating, constant and accelerating expansionsp. 95
Accelerating Universep. 96
The Tully-Fisher formula: Nonexistence of halo dark matterp. 97
The Geodesic Equationp. 98
Equations of motionp. 99
The Tully-Fisher lawp. 102
Cosmological redshift analysisp. 104
The redshift formulap. 104
Particular casesp. 105
Conclusionsp. 106
Verification of the classical general relativity testsp. 106
Comparison with general relativityp. 106
Gravitational redshiftp. 109
Motion in a centrally symmetric gravitational fieldp. 111
Deflection of light in a gravitational fieldp. 117
Gravitational wavesp. 120
Mathematical Conventionsp. 123
Components of the Ricci tensorp. 124
Integration of the Universe Expansion Equationp. 127
Indexp. 129
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