Book description
Table of contents
 Cover
 Title Page
 Contents
 Preface
 Historical Perspective

Chapter 1: A Brief Review of Special Relativity
 1.1 Introduction
 1.2 Some Common Definitions
 1.3 The Constancy of Velocity of Light
 1.4 The Postulates of Special Relativity
 1.5 Interval
 1.6 Lorentz Transformation
 1.7 Kinematic Consequences of Lorentz Transformation
 1.8 Light Cone
 1.9 FourVectors
 1.10 Relativistic Mass
 1.11 Electromagnetic Field Tensor
 1.12 Covariant Form of Maxwell’s Equations
 1.13 Photons and Neutrinos
 Problems

Chapter 2: Tensor Analysis and Riemannian Geomtry

Part I: Line Element
 2.1 Riemannian Space
 2.2 Transformation of Coordinates
 2.3 Contravariant and Covariant Vectors
 2.4 Summation Convention
 2.5 The Metric
 2.6 The Metric as a Tensor
 2.7 Contravariant, Covariant, and Mixed Tensors
 2.8 Multiplication of Tensors—Inner and Outer Products andContraction
 2.9 Quotient Law of Tensors
 2.10 Fundamental Tensors: gμv, gμv, and gμv
 2.11 Raising and Lowering of Indices
 Problems
 Part II: Geodesic Curves—Covariant Differentiation

Part III: Curvature Tensor
 2.18 Riemannian Coordinates
 2.19 Riemann–Christoffel Curvature Tensor
 2.20 Symmetries and AntiSymmetries of Curvature Tensor
 2.21 Number of Independent Components of the Curvature Tensor Rλμνσ
 2.22 The Bianchi Identities
 2.23 The Ricci Tensor
 2.24 The Contracted Binachi Identities or the Einstein Tensor
 2.25 Uniform Vector Field
 2.26 The Condition for Flat Space–Time
 2.27 Parallel Displacement and Affine Connections
 2.28 Affine Connections for the Covariant Vector
 2.29 Affine Connections and the Metric Tensor
 2.30 Parallel Displacement and Covariant Differentiation
 2.31 EnergyMomentum Tensor for a Perfect Fluid
 Problems

Part I: Line Element

Chapter 3: Einstein’s Field Equations
 3.1 Introduction
 3.2 Principle of Equivalence
 3.3 Principle of Covariance
 3.4 Newtonian Equation of Motion as an Approximation of Geodesic Equations
 3.5 Heuristic Derivation of Einstein’s Field Equations
 3.6 Einstein’s Field Equations by Variational Technique
 3.7 Fundamental Hypotheses and Postulates of General Relativity
 3.8 Poisson’s Equation as Approximation of Einstein’s Field Equations. Evaluation of Constant k
 Problems
 Chapter 4: Einstein’s Law of Gravitation in Empty Space—Schwarzschild Solution
 Chapter 5: Einstein’s Field Equations for NonEmpty Space

Chapter 6: Gravitational Waves
 6.1 Introduction
 6.2 Weak Gravitational Field, Linearized Field Equations
 6.3 Plane Wave Solutions
 6.4 Behaviour of a Massive Particle as a Gravitational Wave Passes
 6.5 The Detection of Gravitational Waves
 6.6 Quadrupolar Nature of Gravitational Waves
 6.7 The Emission of Gravitational Waves
 6.8 Experimental Support for Gravitational Waves
 Problems

Chapter 7: Black Holes
 7.1 Introduction
 7.2 Schwarzschild Black Holes—Singularities
 7.3 Kruskal Coordinates
 7.4 The Kerr Metric in Boyer–Lindquist Coordinates
 7.5 Frame Dragging—Lense–Thirring Effect
 7.6 Energy Extraction from a Rotating Black Hole. Penrose Process
 7.7 The Reissner–Nordström Solution
 7.8 Evidence for the Existence of Black Holes
 Problems

Chapter 8: Cosmology
 8.1 Introduction
 8.2 The Cosmological Principle and Weyl’s Postulate
 8.3 A Spatial Metric Incorporating Homogeneity and Isotropy
 8.4 Spaces of Positive, Negative, and Zero Curvature
 8.5 Static Cosmological Models
 8.6 The RobertsonWalker Metric. Friedmann Equations
 8.7 NonStatic Cosmological Models. Time Evolution of Universe
 8.8 Useful Terminology
 8.9 The RedShift
 8.10 Preliminaries for Early Universe
 8.11 The Standard Model of Early Universe
 8.12 The Age of the Universe
 8.13 Cosmological Constant in Einstein’s Field Equations
 8.14 Cosmic Microwave Background Radiation
 Problems
 Chapter 9: Astrophysics
 Notes
 Epilogue
 Bibliography
 Copyright
 Back Cover
Product information
 Title: General theory of Relativity
 Author(s):
 Release date: January 2013
 Publisher(s): Pearson India
 ISBN: 9789332516359
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