Tensors, Relativity, and Cosmology

ISBN-10: 012200681X
ISBN-13: 9780122006814
Edition: 2005
List price: $92.95 Buy it from $29.19
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Description: This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity  More...

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Book details

List price: $92.95
Copyright year: 2005
Publisher: Elsevier Science & Technology Books
Publication date: 3/21/2005
Binding: Paperback
Pages: 320
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.518
Language: English

This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity 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, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.

Introduction
Tensor Algebra
Notation and Systems of Numbers
Introduction and Basic Concepts
Symmetric and Antisymmetric Systems
Operations with Systems
Addition and Subtraction of Systems
Direct Product of Systems
Contraction of Systems
Composition of Systems
Summation Convention
Unit Symmetric and Antisymmetric Systems 3 Vector Spaces
Introduction and Basic Concepts
Defnition of a Vector Space
The Euclidean Metric Space
The Riemannian Spaces 4 Definitions of Tensors
Transformations of Variables
Contravariant Vectors
Covariant Vectors
Invariants (Scalars)
Contravariant Tensors
Covariant Tensors
Mixed Tensors
Symmetry Properties of Tensors
Symmetric and Antisymmetric Parts of Tensors
Tensor Character of Systems 5 Relative Tensors
Introduction and Definitions
Unit Antisymmetric Tensors
Vector Product in Three Dimensions
Mixed Product in Three Dimensions
Orthogonal Coordinate Transformations
Rotations of Descartes Coordinates
Translations of Descartes Coordinates
Inversions of Descartes Coordinates
Axial Vectors and Pseudoscalars in Descartes Coordinates 6 The Metric Tensor
Introduction and Definitions
Associated Vectors and Tensors
Arc Length of Curves. Unit Vectors
Angles between Vectors
Schwarz Inequality
Orthogonal and Physical Vector Coordinates 7 Tensors as Linear Operators
Tensor Analysis
Tensor Derivatives
Differentials of Tensors
Differentials of Contravariant Vectors
Differentials of Covariant Vectors
Covariant Derivatives
Covariant Derivatives of Vectors
Covariant Derivatives of Tensors
Properties of Covariant Derivatives
Absolute Derivatives of Tensors
Christoffel Symbols
Properties of Christoff Symbols
Relation to the Metric Tensor
Differential Operators
The Hamiltonian r-Operator
Gradient of Scalars
Divergence of Vectors and Tensors
Curl of Vectors
Laplacian of Scalars and Tensors
Integral Theorems for Tensor Fields
Stokes Theorem
Gauss Theorem
Geodesic Lines
Lagrange Equations
Geodesic Equations
The Curvature Tensor
Definition of the Curvature Tensor
Properties of the Curvature Tensor
Commutator of Covariant Derivatives
Ricci Tensor and Scalar
Curvature Tensor Components
Special Theory of Relativity
Relativistic Kinematics
The Principle of Relativity
Invariance of the Speed of Light
The Interval between Events
Lorentz Transformations
Velocity and Acceleration Vectors
Relativistic Dynamics
Lagrange Equations
Energy-Momentum Vector
Introduction and Definitions
Transformations of Energy-Momentum
Conservation of Energy-Momentum
Angular Momentum Tensor
Electromagnetic Fields
Electromagnetic Field Tensor
Gauge Invariance
Lorentz Transformations and Invariants
Electromagnetic Field Equations
Electromagnetic Current Vector
Maxwell Equations
Electromagnetic Potentials
Energy-Momentum Tensor
General Theory of Relativity
Gravitational Fields
Introduction
Time Intervals and Distances
Particle Dynamics
Electromagnetic Field Equations
Gravitational Field Equations
The Action Integral
Action for Matter Fields
Einstein Field Equations
Solutions of Field Equations
The Newton Law
The Schw

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