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