Introduction to General Relativity and the Cosmological Constant ProblemNova Publishers, 2007 - Počet stran: 213 This book is an introductory text in General Relativity, while also focusing some solutions to the cosmological constant problem, which consists in an amazing 100 orders of magnitude discrepancy between the value of this constant in the present Universe, and its estimated value in the very early epoch. The author suggests that the constant is in fact, a time-varying function of the age of the Universe. The book offers a wealth of cosmological models, treats up to date findings, like the verification of the Lense-Thirring effect in the year 2004, and the recently published research by Cooperstock and Tieu (2005) suggesting that "dark" matter is not a necessary concept in order to explain the rotational velocities of stars around galaxies' nuclei. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course. |
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3 | |
7 | |
9 | |
Tensors in Riemann Spaces | 11 |
22 Christoffel Symbols | 13 |
23 Covariant Derivative | 14 |
24 Curvature Tensors | 15 |
INTRODUCTION TO GENERAL RELATIVITY | 19 |
73 Constant Deceleration Parameter Models | 84 |
74 Cosmological RedShift | 86 |
75 Hubbles Law | 88 |
77 Inflation | 89 |
78 Plancks Universe and the Aproblem | 91 |
79 A WhiteHoleRobertsonWalkers Universe | 92 |
ENERGY OF THE VACUUM AND THE 𝛬 UNIVERSE | 97 |
The 𝛬 Problem and Its Solution | 99 |
Basic Theory | 21 |
32 EnergyMomentum Tensor | 22 |
33 Tij for the Electromagnetic Field | 24 |
34 Einsteins Field Equations | 25 |
35 Introducing the Cosmological Constant | 27 |
36 Reduction of CRT into Newtonian Physics | 29 |
37 The Geodesies Equation a Derivation | 32 |
38 Gravitational Radiation | 33 |
Schwarzschilcs Metric and Classical Experimental Tests | 35 |
42 The Motion of Planets and Perihelion Precession | 40 |
43 Propagation of Light near Gravitational Fields | 44 |
44 Spectral Displacement Due to Gravitational Cause | 46 |
45 Other Verifications of the GRT | 47 |
Complements of Tensor Calculus and General Relativity Optional Study | 51 |
52 Parallel Transport in Riemann Space | 53 |
53 FermiWalkers Transport | 54 |
54 Lie Derivative | 55 |
55 Isometrics | 57 |
56 Stationary and Static Fields | 59 |
INTRODUCTION TO RELATIVISTIC COSMOLOGY | 61 |
Digression into Philosophical and Mathematical Matters Optional Study | 63 |
62 Objections to Newtons Cosmology | 64 |
63 Machs Principle | 66 |
64 The Potential for Gravitation | 68 |
65 Equivalence Principle | 70 |
66 The Principles of General Relativity Covariance and Simplicity | 72 |
67 Principles of Cosmic Time and Correspondence | 73 |
RobertsonWalkers Metric | 77 |
72 Einsteins Field Equations for Cosmology | 80 |
82 Generalized Large Number Hypothesis | 100 |
83 Raychaudhuris Equation and 𝛬 variable | 101 |
84 Berman Model with Modified Energy Momentum Conservation | 102 |
85 AbdelRahmanArbabBerman Model | 105 |
86 Chen and Wus Model | 107 |
Energy of the Universe and the 𝛬 Problem | 109 |
92 The Energy of R Ws Universe | 110 |
94 Guessing a Solution Anew for the 𝛬 Problem | 111 |
95 Comment on the 𝛬 Problem | 112 |
96 BransDicke Relation | 113 |
97 Equation of State for the Very Early Universe | 115 |
98 Creation of the Universe out of Nothing | 116 |
99 Cosmological Parameters | 118 |
910 Gravitational Density with 𝛬 Term | 119 |
Miscellaneous Cosmological Models | 123 |
102 BransDicke Cosmology with Variable Lambda | 128 |
103 Model with Time Varying Fine Structure Constant 1 | 131 |
104 Model with Time Varying Fine Structure Constant 2 | 134 |
105 Model with Time Varying Fine Structure Constant 3 | 136 |
106 The Machian Universe Revisited | 138 |
107 Dark Matter as Neutrinos with TimeVarying Mass | 143 |
CONCLUDING REMARKS | 149 |
Concluding Remarks | 151 |
112 Review of the Text | 152 |
Appendix I Gravitomagnetism | 155 |
Appendix II Absence of Dark Matter in Galaxies | 167 |
References and Suggested Bibliography | 171 |
209 | |
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2nd rank acceleration Alamos Archives http://arxiv.org/abs/gr astr Barrow Berman black hole black-hole Brans-Dicke relation calculation Chapter Christoffel symbols constant deceleration parameter contravariant Cooperstock coordinate system cosmic pressure cosmological constant Cosmological Models covariant derivative deceleration parameter define ds² dx'i early Universe Einstein's field equations energy density energy-momentum tensor Fine Structure Constant galaxies geodesic geometry given Gomide gravitational field gravitomagnetic inertial Journal of Theoretical lambda Lense-Thirring metric Lett Lie derivative Mach's Principle Machian Machian Universe Magueijo mass Mathematical matter metric tensor Minkowski's neutrinos Newton's Newtonian null obtain particle Phys Physical Review Planck's potential present Universe problem Proc Quantum Gravity radius Relativistic result Robertson-Walker's metric rotating scalar scale-factor Schwarzschild's metric Section sin² solution space spacetime Special Relativity speed of light Structure Constant term Theoretical Physics theory total energy transformation valid variable variation vector white-hole zero дхі