Tensors, relativity, and cosmology:
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case fo...
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam ; Boston ; Heidelberg ; London und 8 weitere
Elsevier
[2015]
|
| Ausgabe: | Second Edition |
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Zusammenfassung: | Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. |
| Beschreibung: | xii, 263 Seiten Diagramme |
| ISBN: | 9780128033975 |
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| adam_text | TENSORS,
RELATIVITY, AND
COSMOLOGY
Second Edition
Mirjana Dalarsson and Nils Dalarsson
Relativity, gravitation, and cosmology are all broad areas of modern physics, with an
extensive selection of adequate textbooks and monographs for advanced graduate
students and professionals working in these fields. Due to some features of the theory
of relativity that are very counterintuitive and intriguing for the general public, there
are also quite a few books which take a general descriptive approach appropriate for
readers with no background in physics. However, intermediate books, intended for
senior undergraduate students or new graduate students, are quite rare. It seems
to be generally assumed that the new concepts of both physics and mathematics
involved in these subjects are too complex to permit a straightforward introduction.
University students trying to grasp these exciting and foundational ideas will encoun-
ter hand-waving phrases in the literature allowing that something can be derived
from something else by some straightforward although tedious algebra. If a student
cannot readily reproduce such straightforward algebra, which is most often the case,
the usual reaction is to accept the claim as a fact, but at the price of lost satisfaction
in understanding the subject.
This book strives to bridge the gap between textbooks used in a core university
program consisting typically of basic calculus and general physics and the advanced
graduate level books in tensor calculus, relativity, and cosmology. It was conceived
to help students master the background necessary for advanced study without the
tedious and time-consuming effort to review the relevant portions of advanced text-
books. More lengthy and algebraic manipulations are outlined in sufficient detail that
they can be followed by an interested senior undergraduate student or a beginning
graduate student, with minimal risk of getting lost.
This fully revised and updated second edition includes new material on relativistic
effects, such as the behavior of clocks and measuring rods in motion, relativistic
addition of velocities, and the twin paradox, as well as new material on gravitational
waves, such as weak-field solutions, propagation of gravitational waves, generation of
gravitational waves, and detection of gravitational waves.
Table of Contents
Preface xi
P
1 Introduction 1
PART 1 Tensor Algebra 3
2 Notation and Systems of Numbers 5
2.1 Introduction and Basic Concepts 5
2.2 Symmetric and Antisymmetric Systems 6
2.3 Operations with Systems 7
2.4 Summation Convention 9
2.5 Unit Symmetric and Antisymmetric Systems 10
3 Vector Spaces 13
3.1 Introduction and Basic Concepts 13
3.2 Definition of a Vector Space 14
3.3 The Euclidean Metric Space 15
3.4 The Riemannian Spaces 15
4 Definitions of Tensors 21
4.1 Transformations of Variables 21
4.2 Contravariant Vectors 21
4.3 Covariant Vectors 22
4.4 Invariants (Scalars) 22
4.5 Contravariant Tensors 23
4.6 Covariant Tensors 23
4.7 Mixed Tensors 24
V
vi Table of Contents
4.8 Symmetry Properties of Tensors 24
4.9 Symmetric and Antisymmetric Parts of Tensors 25
4.10 Tensor Character of Systems 26
5 Relative Tensors 29
5.1 Introduction and Definitions 29
5.2 Unit Antisymmetric Tensors 29
5.3 Vector Product in Three Dimensions 31
5.4 Mixed Product in Three Dimensions 33
5.5 Orthogonal Coordinate Transformations 34
6 The Metric Tensor 39
6.1 Introduction and Definitions 39
6.2 Associated Vectors and Tensors 41
6.3 Arc Length of Curves: Unit Vectors 43
6.4 Angles between Vectors 44
6.5 Schwarz Inequality 45
6.6 Orthogonal and Physical Vector Coordinates 46
7 Tensors as Linear Operators 49
PART 2 Tensor Analysis 53
8 Tensor Derivatives 55
8.1 Differentials of Tensors 55
8.2 Covariant Derivatives 58
8.3 Properties of Covariant Derivatives 60
8.4 Absolute Derivatives of Tensors 61
9 Christoffel Symbols 63
9.1 Properties of Christoffel Symbols 63
9.2 Relation to the Metric Tensor 65
Table of Contents vii
10 Differential Operators 69
10.1 The Hamiltonian V-Operator 69
10.2 Gradient of Scalars 69
10.3 Divergence of Vectors and Tensors 70
10.4 Curl of Vectors 71
10.5 Laplacian of Scalars and Tensors 72
10.6 Integral Theorems for Tensor Fields 73
11 Geodesic Lines 77
11.1 Lagrange Equations 77
11.2 Geodesic Equations 79
12 The Curvature Tensor 83
12.1 Definition of the Curvature Tensor 83
12.2 Properties of the Curvature Tensor 85
12.3 Commutator of Covariant Derivatives 87
12.4 Ricci Tensor and Scalar 89
12.5 Curvature Tensor Components 89
PART 3 Special Theory of Relativity 93
13 Relativistic Kinematics 95
13.1 The Principle of Relativity 95
13.2 Invariance of the Speed of Light 95
13.3 The Interval between Events 96
13.4 Lorentz Transformations 99
13.5 Velocity and Acceleration Vectors 102
14 Relativistic Phenomena 105
14.1 Introduction 105
14.2 Time Dilatation 105
14.3 Length Contraction 106
viii Table of Contents
14.4 Relativistic Addition of Velocities 108
14.5 The Twin Paradox 109
15 Relativistic Dynamics 111
15.1 Lagrange Equations 111
15.2 Energy-Momentum Vector 113
15.3 Angular Momentum Tensor 118
16 Electromagnetic Fields 121
16.1 Electromagnetic Field Tensor 121
16.2 Gauge Invariance 125
16.3 Lorentz Transformations and Invariants 126
17 Electromagnetic Field Equations 131
17.1 Electromagnetic Current Vector 131
17.2 Maxwell Equations 133
17.3 Electromagnetic Potentials 137
17.4 Energy-Momentum Tensor 138
PART 4 General Theory of Relativity 145
18 Gravitational Fields 147
18.1 Introduction 147
18.2 Time Intervals and Distances 148
18.3 Particle Dynamics 150
18.4 Electromagnetic Field Equations 153
19 Gravitational Field Equations 157
19.1 The Action Integral 157
19.2 Action for Matter Fields 162
19.3 Einstein Field Equations 166
Table of Contents ix
20 Solutions of Field Equations 171
20.1 The Newton Law 171
20.2 The Schwarzschild Solution 172
21 Applications of the Schwarzschild Metric 183
21.1 The Perihelion Advance 183
21.2 The Black Holes 190
22 Gravitational Waves 197
22.1 Introduction 197
22.2 Linearized Einstein Field Equations 197
22.3 Plane-wave Solutions 202
22.4 Effects of Gravitational Waves on Particles 205
22.5 Generation of Gravitational Radiation 208
PART 5 Elements of Cosmology 211
23 The Robertson-Walker Metric 213
23.1 Introduction and Basic Observations 213
23.2 Metric Definition and Properties 214
23.3 The Hubble Law 220
23.4 The Cosmological Red Shifts 221
24 The Cosmic Dynamics 225
24.1 The Einstein Tensor 225
24.2 Friedmann Equations 233
25 Non-static Models of the Universe 237
25.1 Solutions of Friedmann Equations 237
25.2 Closed or Open Universe 241
25.3 Newtonian Cosmology 242
x Table of Contents
26 The Quantum Cosmology 247
26.1 Introduction 247
26.2 Wheeler-De Witt Equation 248
26.3 The Wave Function of the Universe 251
Bibliography 255
Index 257
|
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| spelling | Dalarsson, Mirjana Verfasser (DE-588)1011508117 aut Tensors, relativity, and cosmology M. Dalarsson, Ericsson Research and Development, Stockholm, Sweden, N. Dalarsson, Royal Institute of Technology, Stockholm, Sweden Second Edition Amsterdam ; Boston ; Heidelberg ; London und 8 weitere Elsevier [2015] © 2015 xii, 263 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Kosmologie (DE-588)4114294-9 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Tensoranalysis (DE-588)4204323-2 s DE-604 Relativitätstheorie (DE-588)4049363-5 s Kosmologie (DE-588)4114294-9 s Dalarsson, Nils Verfasser (DE-588)1011672596 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028195710&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028195710&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Tensors, relativity, and cosmology |
| title_auth | Tensors, relativity, and cosmology |
| title_exact_search | Tensors, relativity, and cosmology |
| title_full | Tensors, relativity, and cosmology M. Dalarsson, Ericsson Research and Development, Stockholm, Sweden, N. Dalarsson, Royal Institute of Technology, Stockholm, Sweden |
| title_fullStr | Tensors, relativity, and cosmology M. Dalarsson, Ericsson Research and Development, Stockholm, Sweden, N. Dalarsson, Royal Institute of Technology, Stockholm, Sweden |
| title_full_unstemmed | Tensors, relativity, and cosmology M. Dalarsson, Ericsson Research and Development, Stockholm, Sweden, N. Dalarsson, Royal Institute of Technology, Stockholm, Sweden |
| title_short | Tensors, relativity, and cosmology |
| title_sort | tensors relativity and cosmology |
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