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Umfang: 1 online resource (276 p.)

Ausgabe: 2nd ed.

ISBN: 9780128034019 , 0128034017 , 9780128033975 , 0128033975

Inhalt: 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 relativi

Anmerkung: Description based upon print version of record , 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 , 13.5 Velocity and Acceleration Vectors

Sprache: Englisch

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Umfang: 1 Online-Ressource (xii, 263 Seiten) : , Diagramme.

Ausgabe: Second edition

ISBN: 978-0-12-803401-9

Inhalt: 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

Weitere Ausg.: Erscheint auch als Druck-Ausgabe ISBN 978-0-12-803397-5

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Tensoranalysis ; Relativitätstheorie ; Kosmologie

URL: Volltext  (URL des Erstveröffentlichers)

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URL: Volltext  (URL des Erstveröffentlichers)

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