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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Academic Press,
2015.
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| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Tensors, Relativity, and Cosmology; Copyright; Table of Contents; Preface; Chapter 1: Introduction; Part 1: Tensor Algebra; Chapter 2: Notation and Systems of Numbers; 2.1 Introduction and Basic Concepts; 2.2 Symmetric and Antisymmetric Systems; 2.3 Operations with Systems; 2.3.1 Addition and Subtraction of Systems; 2.3.2 Direct Product of Systems; 2.3.3 Contraction of Systems; 2.3.4 Composition of Systems; 2.4 Summation Convention; 2.5 Unit Symmetric and Antisymmetric Systems; Chapter 3: Vector Spaces; 3.1 Introduction and Basic Concepts; 3.2 Definition of a Vector Space
- 3.3 The Euclidean Metric Space3.4 The Riemannian Spaces; Chapter 4: Definitions of Tensors; 4.1 Transformations of Variables; 4.2 Contravariant Vectors; 4.3 Covariant Vectors; 4.4 Invariants (Scalars); 4.5 Contravariant Tensors; 4.6 Covariant Tensors; 4.7 Mixed Tensors; 4.8 Symmetry Properties of Tensors; 4.9 Symmetric and Antisymmetric Parts of Tensors; 4.10 Tensor Character of Systems; Chapter 5: Relative Tensors; 5.1 Introduction and Definitions; 5.2 Unit Antisymmetric Tensors; 5.3 Vector Product in Three Dimensions; 5.4 Mixed Product in Three Dimensions
- 5.5 Orthogonal Coordinate Transformations5.5.1 Rotations of Descartes Coordinates; 5.5.2 Translations of Descartes Coordinates; 5.5.3 Inversions of Descartes Coordinates; 5.5.4 Axial Vectors and Pseudoscalars; Chapter 6: The Metric Tensor; 6.1 Introduction and Definitions; 6.2 Associated Vectors and Tensors; 6.3 Arc Length of Curves: Unit Vectors; 6.4 Angles between Vectors; 6.5 Schwarz Inequality; 6.6 Orthogonal and Physical Vector Coordinates; Chapter 7: Tensors as Linear Operators; Part 2: Tensor Analysis; Chapter 8: Tensor Derivatives; 8.1 Differentials of Tensors
- 8.1.1 Differentials of Contravariant Vectors8.1.2 Differentials of Covariant Vectors; 8.2 Covariant Derivatives; 8.2.1 Covariant Derivatives of Vectors; 8.2.2 Covariant Derivatives of Tensors; 8.3 Properties of Covariant Derivatives; 8.4 Absolute Derivatives of Tensors; Chapter 9: Christoffel Symbols; 9.1 Properties of Christoffel Symbols; 9.2 Relation to the Metric Tensor; Chapter 10: Differential Operators; 10.1 The Hamiltonian -Operator; 10.2 Gradient of Scalars; 10.3 Divergence of Vectors and Tensors; 10.4 Curl of Vectors; 10.5 Laplacian of Scalars and Tensors
- 10.6 Integral Theorems for Tensor Fields10.6.1 Stokes Theorem; 10.6.2 Gauss Theorem; Chapter 11: Geodesic Lines; 11.1 Lagrange Equations; 11.2 Geodesic Equations; Chapter 12: The Curvature Tensor; 12.1 Definition of the Curvature Tensor; 12.2 Properties of the Curvature Tensor; 12.3 Commutator of Covariant Derivatives; 12.4 Ricci Tensor and Scalar; 12.5 Curvature Tensor Components; Part 3: Special Theory of Relativity; Chapter 13: Relativistic Kinematics; 13.1 The Principle of Relativity; 13.2 Invariance of the Speed of Light; 13.3 The Interval between Events; 13.4 Lorentz Transformations