Relativity Demystified [PDF] - Oceanhawk

*********************************************************************************** ~~~~~~~~~~~~~~~~Relativity Demystified | 370 pages | PDF | 5.22 MB~~~~~~~~~~~~~~~~~ *********************************************************************************** Now anyone can grasp Einstein's great theory of relativity -- without formal training, unlimited time, or a genius IQ. In Relativity Demystified, theoretical physicists (and student-savvy authors) David McMahon and Paul Ansing provide an effective, illuminating, and entertaining way to learn the essentials and formulas of Einstein's theories. With Relativity Demystified, you master the subject one step at a time—at your own speed. This unique self-teaching guide offers problems at the end of each chapter and part to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book. This fast and entertaining self-teaching course makes it much easier to: CONTENTS Preface xi CHAPTER 1 A Quick Review of Special Relativity 1 Frame of Reference 5 Clock Synchronization 5 Inertial Frames 6 Galilean Transformations 7 Events 7 The Interval 8 Postulates of Special Relativity 9 Three Basic Physical Implications 13 Light Cones and Spacetime Diagrams 17 Four Vectors 19 Relativistic Mass and Energy 20 Quiz 21 CHAPTER 2 Vectors, One Forms, and the Metric 23 Vectors 23 New Notation 25 Four Vectors 27 The Einstein Summation Convention 28 Tangent Vectors, One Forms, and the Coordinate Basis 29 Coordinate Transformations 31 The Metric 32 The Signature of a Metric 36 The Flat Space Metric 37 The Metric as a Tensor 37 Index Raising and Lowering 38 Index Gymnastics 41 The Dot Product 42 Passing Arguments to the Metric 43 Null Vectors 45 The Metric Determinant 45 Quiz 45 CHAPTER 3 More on Tensors 47 Manifolds 47 Parameterized Curves 49 Tangent Vectors and One Forms, Again 50 Tensors as Functions 53 Tensor Operations 54 The Levi-Cevita Tensor 59 Quiz 59 CHAPTER 4 Tensor Calculus 60 Testing Tensor Character 60 The Importance of Tensor Equations 61 The Covariant Derivative 62 The Torsion Tensor 72 The Metric and Christoffel Symbols 72 The Exterior Derivative 79 The Lie Derivative 81 The Absolute Derivative and Geodesics 82 The Riemann Tensor 85 The Ricci Tensor and Ricci Scalar 88 The Weyl Tensor and Conformal Metrics 90 Quiz 91 CHAPTER 5 Cartan’s Structure Equations 93 Introduction 93 Holonomic (Coordinate) Bases 94 Nonholonomic Bases 95 Commutation Coefficients 96 Commutation Coefficients and Basis One Forms 98 Transforming between Bases 100 A Note on Notation 103 Cartan’s First Structure Equation and the Ricci Rotation Coefficients 104 Computing Curvature 112 Quiz 120 CHAPTER 6 The Einstein Field Equations 122 Equivalence of Mass in Newtonian Theory 123 Test Particles 126 The Einstein Lift Experiments 126 The Weak Equivalence Principle 130 The Strong Equivalence Principle 130 The Principle of General Covariance 131 Geodesic Deviation 131 The Einstein Equations 136 The Einstein Equations with Cosmological Constant 138 An Example Solving Einstein’s Equations in 2 + 1 Dimensions 139 Energy Conditions 152 Quiz 152 CHAPTER 7 The Energy-Momentum Tensor 155 Energy Density 156 Momentum Density and Energy Flux 156 Stress 156 Conservation Equations 157 Dust 158 Perfect Fluids 160 Relativistic Effects on Number Density 163 More Complicated Fluids 164 Quiz 165 CHAPTER 8 Killing Vectors 167 Introduction 167 Derivatives of Killing Vectors 177 Constructing a Conserved Current with Killing Vectors 178 Quiz 178 CHAPTER 9 Null Tetrads and the Petrov Classification 180 Null Vectors 182 A Null Tetrad 184 Extending the Formalism 190 Physical Interpretation and the Petrov Classification 193 Quiz 201 CHAPTER 10 The Schwarzschild Solution 203 The Vacuum Equations 204 A Static, Spherically Symmetric Spacetime 204 The Curvature One Forms 206 Solving for the Curvature Tensor 209 The Vacuum Equations 211 The Meaning of the Integration Constant 214 The Schwarzschild Metric 215 The Time Coordinate 215 The Schwarzschild Radius 215 Geodesics in the Schwarzschild Spacetime 216 Particle Orbits in the Schwarzschild Spacetime 218 The Deflection of Light Rays 224 Time Delay 229 Quiz 230 CHAPTER 11 Black Holes 233 Redshift in a Gravitational Field 234 Coordinate Singularities 235 Eddington-Finkelstein Coordinates 236 The Path of a Radially Infalling Particle 238 Eddington-Finkelstein Coordinates 239 Kruskal Coordinates 242 The Kerr Black Hole 244 Frame Dragging 249 The Singularity 252 A Summary of the Orbital Equations for the Kerr Metric 252 Further Reading 253 Quiz 254 CHAPTER 12 Cosmology 256 The Cosmological Principle 257 A Metric Incorporating Spatial Homogeneity and Isotropy 257 Spaces of Positive, Negative, and Zero Curvature 262 Useful Definitions 264 The Robertson-Walker Metric and the Friedmann Equations 267 Different Models of the Universe 271 Quiz 276 CHAPTER 13 Gravitational Waves 279 The Linearized Metric 280 Traveling Wave Solutions 284 The Canonical Form and Plane Waves 287 The Behavior of Particles as a Gravitational Wave Passes 291 The Weyl Scalars 294 Review: Petrov Types and the Optical Scalars 295 pp Gravity Waves 297 Plane Waves 301 The Aichelburg-Sexl Solution 303 Colliding Gravity Waves 304 The Effects of Collision 311 More General Collisions 312 Nonzero Cosmological Constant 318 Further Reading 321 Quiz 322 Final Exam 323 Quiz and Exam Solutions 329 References and Bibliography 333 Index 337 =================================================================================== *********************************************************************************** **********In order to keep files alive please seed until a ratio of 1:1************ ****************************Thank you ~ Oceanhawk :)******************************* *********************************************************************************** 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