Introduction to General Relativity and the Cosmological Constant Problem

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Nova 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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Obsah

Tensors in Amorphous Spaces
3
13 Algebraic Operations with Tensors
7
14 Final Observations
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
Index
209
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