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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 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… More accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.Less

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Book details

List price: $92.95 Copyright year: 2005 Publisher: Elsevier Science & Technology Publication date: 4/29/2005 Binding: Paperback Pages: 320 Size: 6.25" wide x 9.00" long x 0.75" tall Weight: 1.298 Language: English

AuthorTable of Contents

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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