Relativity Demystified

ISBN-10: 0071455450
ISBN-13: 9780071455459
Edition: 2006
List price: $25.00 Buy it from $3.00
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Description: This guide to Einstein's theory of relativity presents an overview of the essentials and formulas of Einstein's theory, and focuses on quick definitions and demonstrations of the procedures needed to solve problems.

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Book details

List price: $25.00
Copyright year: 2006
Publisher: McGraw-Hill Professional Publishing
Publication date: 12/23/2005
Binding: Paperback
Pages: 344
Size: 7.25" wide x 9.00" long x 1.00" tall
Weight: 1.606
Language: English

This guide to Einstein's theory of relativity presents an overview of the essentials and formulas of Einstein's theory, and focuses on quick definitions and demonstrations of the procedures needed to solve problems.

Preface
A Quick Review of Special Relativity
Frame of Reference
Clock Synchronization
Inertial Frames
Galilean Transformations
Events
The Interval
Postulates of Special Relativity
Three Basic Physical Implications
Light Cones and Spacetime Diagrams
Four Vectors
Relativistic Mass and Energy
Quiz
Vectors, One Forms, and the Metric
Vectors
New Notation
Four Vectors
The Einstein Summation Convention
Tangent Vectors, One Forms, and the Coordinate Basis
Coordinate Transformations
The Metric
The Signature of a Metric
The Flat Space Metric
The Metric as a Tensor
Index Raising and Lowering
Index Gymnastics
The Dot Product
Passing Arguments to the Metric
Null Vectors
The Metric Determinant
Quiz
More on Tensors
Manifolds
Parameterized Curves
Tangent Vectors and One Forms, Again
Tensors as Functions
Tensor Operations
The Levi-Cevita Tensor
Quiz
Tensor Calculus
Testing Tensor Character
The Importance of Tensor Equations
The Covariant Derivative
The Torsion Tensor
The Metric and Christoffel Symbols
The Exterior Derivative
The Lie Derivative
The Absolute Derivative and Geodesics
The Riemann Tensor
The Ricci Tensor and Ricci Scalar
The Weyl Tensor and Conformal Metrics
Quiz
Cartan's Structure Equations
Introduction
Holonomic (Coordinate) Bases
Nonholonomic Bases
Commutation Coefficients
Commutation Coefficients and Basis One Forms
Transforming between Bases
A Note on Notation
Cartan's First Structure Equation and the Ricci Rotation Coefficients
Computing Curvature
Quiz
The Einstein Field Equations
Equivalence of Mass in Newtonian Theory
Test Particles
The Einstein Lift Experiments
The Weak Equivalence Principle
The Strong Equivalence Principle
The Principle of General Covariance
Geodesic Deviation
The Einstein Equations
The Einstein Equations with Cosmological Constant
An Example Solving Einstein's Equations in 2 + 1 Dimensions
Energy Conditions
Quiz
The Energy-Momentum Tensor
Energy Density
Momentum Density and Energy Flux
Stress
Conservation Equations
Dust
Perfect Fluids
Relativistic Effects on Number Density
More Complicated Fluids
Quiz
Killing Vectors
Introduction
Derivatives of Killing Vectors
Constructing a Conserved Current with Killing Vectors
Quiz
Null Tetrads and the Petrov Classification
Null Vectors
A Null Tetrad
Extending the Formalism
Physical Interpretation and the Petrov Classification
Quiz
The Schwarzschild Solution
The Vacuum Equations
A Static, Spherically Symmetric Spacetime
The Curvature One Forms
Solving for the Curvature Tensor
The Vacuum Equations
The Meaning of the Integration Constant
The Schwarzschild Metric
The Time Coordinate
The Schwarzschild Radius
Geodesics in the Schwarzschild Spacetime
Particle Orbits in the Schwarzschild Spacetime
The Deflection of Light Rays
Time Delay
Quiz
Black Holes
Redshift in a Gravitational Field
Coordinate Singularities
Eddington-Finkelstein Coordinates
The Path of a Radially Infalling Particle
Eddington-Finkelstein Coordinates
Kruskal Coordinates
The Kerr Black Hole
Frame Dragging
The Singularity
A Summary of the Orbital Equations for the Kerr Metric
Further Reading
Quiz
Cosmology
The Cosmological Principle
A Metric Incorporating Spatial Homogeneity and Isotropy
Spaces of Positive, Negative, and Zero Curvature
Useful Definitions
The Robertson-Walker Metric and the Friedmann Equations
Different Models of the Universe
Quiz
Gravitational Waves
The Linearized Metric
Traveling Wave Solutions
The Canonical Form and Plane Waves
The Behavior of Particles as a Gravitational Wave Passes
The Weyl Scalars
Review: Petrov Types and the Optical Scalars
pp Gravity Waves
Plane Waves
The Aichelburg-Sexl Solution
Colliding Gravity Waves
The Effects of Collision
More General Collisions
Nonzero Cosmological Constant
Further Reading
Quiz
Final Exam
Quiz and Exam Solutions
References and Bibliography
Index

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