Relativity and Cosmology: Volume 5 of Modern Classical Physics

by Kip S. Thorne, Roger D. Blandford

Overview

A groundbreaking textbook on twenty-first-century general relativity and cosmology

Kip Thorne and Roger Blandford’s monumental Modern Classical Physics is now available in five stand-alone volumes that make ideal textbooks for individual graduate or advanced undergraduate courses on statistical physics; optics; elasticity and fluid dynamics; plasma physics; and relativity and cosmology. Each volume teaches the fundamental concepts, emphasizes modern, real-world applications, and gives students a physical and intuitive understanding of the subject.

Relativity and Cosmology is an essential introduction to the subject, including remarkable recent advances. Written by award-winning physicists who have made fundamental contributions to the field and taught it for decades, the book differs from most others on the subject in important ways. It highlights recent transformations in our understanding of black holes, gravitational waves, and the cosmos; it emphasizes the physical interpretation of general relativity in terms of measurements made by observers; it explains the physics of the Riemann tensor in terms of tidal forces, differential frame dragging, and associated field lines; it presents an astrophysically oriented description of spinning black holes; it gives a detailed analysis of an incoming gravitational wave’s interaction with a detector such as LIGO; and it provides a comprehensive, in-depth account of the universe’s evolution, from its earliest moments to the present. While the book is designed to be used for a one-quarter or full-semester course, it goes deep enough to provide a foundation for understanding and participating in some areas of cutting-edge research.

• Includes many exercise problems
• Features color figures, suggestions for further reading, extensive cross-references, and a detailed index
• Optional “Track 2” sections make this an ideal book for a one-quarter or one-semester course
• An online illustration package is available to professors

The five volumes, which are available individually as paperbacks and ebooks, are Statistical Physics; Optics; Elasticity and Fluid Dynamics; Plasma Physics; and Relativity and Cosmology.

Product Details

ISBN-13:	9780691207391
Publisher:	Princeton University Press
Publication date:	06/15/2021
Pages:	416
Sales rank:	830,060
Product dimensions:	7.90(w) x 9.90(h) x 0.80(d)

About the Author

Kip S. Thorne, winner of the Nobel Prize in physics, is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation (Princeton) and Black Holes and Time Warps: Einstein’s Outrageous Legacy. Roger D. Blandford, winner of the Crafoord and Shaw prizes in astronomy, is the Luke Blossom Professor in the School of Humanities and Sciences and founding director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University.

Table of Contents

List of Boxes xiii

Preface xv

Contents of Modern Classical Physics, volumes 1-5 xxi

Part VII General Relativity 1151

24 From Special to General Relativity 1153

24.1 Overview 1153

24.2 Special Relativity Once Again 1153

24.2.1 Geometric, Frame-Independent Formulation 1154

24.2.2 Inertial Frames and Components of Vectors, Tensors, and Physical Laws 1156

24.2.3 Light Speed, the Interval, and Spacetime Diagrams 1159

24.3 Differential Geometry in General Bases and in Curved Manifolds 1160

24.3.1 Nonorthonormal Bases 1161

24.3.2 Vectors as Directional Derivatives; Tangent Space; Commutators 1165

24.3.3 Differentiation of Vectors and Tensors; Connection Coefficients 1169

24.3.4 Integration 1174

24.4 The Stress-Energy Tensor Revisited 1176

24.5 The Proper Reference Frame of an Accelerated Observer 1180

24.5.1 Relation to Inertial Coordinates; Metric in Proper Reference Frame; Transport Law for Rotating Vectors 1183

24.5.2 Geodesic Equation for a Freely Falling Particle 1184

24.5.3 Uniformly Accelerated Observer 1186

24.5.4 Rindler Coordinates for Minkowski Spacetime 1187

Bibliographic Note 1190

25 Fundamental Concepts of General Relativity 1191

25.1 History and Overview 1191

25.2 Local Lorentz Frames, the Principle of Relativity, and Einstein's Equivalence Principle 1195

25.3 The Spacetime Metric, and Gravity as a Curvature of Spacetime 1196

25.4 Free-Fail Motion and Geodesics of Spacetime 1200

25.5 Relative Acceleration, Tidal Gravity, and Spacetime Curvature 1206

25.5.1 Newtonian Description of Tidal Gravity 1207

25.5.2 Relativistic Description of Tidal Gravity 1208

25.5.3 Comparison of Newtonian and Relativistic Descriptions 1210

25.6 Properties of the Riemann Curvature Tensor 1213

25.7 Delicacies in the Equivalence Principle, and Some Nongravitational Laws of Physics in Curved Spacetime 1217

25.7.1 Curvature Coupling in the Nongravitational Laws 1218

25.8 The Einstein Field Equation 1221

25.8.1 Geometrized Units 1224

25.9 Weak Gravitational Fields 1224

25.9.1 Newtonian Limit of General Relativity 1225

25.9.2 Linearized Theory 1227

25.9.3 Gravitational Field outside a Stationary, Linearized Source of Gravity 1231

25.9.4 Conservation Laws for Mass, Momentum, and Angular Momentum in Linearized Theory 1237

25.9.5 Conservation Laws for a Strong-Gravity Source 1238

Bibliographic Note 1239

26 Relativistic Stars and Black Holes 1241

26.1 Overview 1241

26.2 Schwarzschild's Spacetime Geometry 1242

26.2.1 The Schwarzschild Metric, Its Connection Coefficients, and Its Curvature Tensors 1242

26.2.2 The Nature of Schwarzschild's Coordinate System, and Symmetries of the Schwarzschild Spacetime 1244

26.2.3 Schwarzschild Spacetime at Radii r >> M: The Asymptotically Flat Region 1245

26.2.4 Schwarzschild Spacetime at r ∼ M 1248

26.3 Static Stars 1250

26.3.1 Birkhoff's Theorem 1250

26.3.2 Stellar Interior 1252

26.3.3 Local Conservation of Energy and Momentum 1255

26.3.4 The Einstein Field Equation 1257

26.3.5 Stellar Models and Their Properties 1259

26.3.6 Embedding Diagrams 1261

26.4 Gravitational Implosion of a Star to Form a Black Hole 1264

26.4.1 The Implosion Analyzed in Schwarzschild Coordinates 1264

26.4.2 Tidal Forces at the Gravitational Radius 1266

26.4.3 Stellar Implosion in Eddington-Finkelstein Coordinates 1267

26.4.4 Tidal Forces at r = 0-The Central Singularity 1271

26.4.5 Schwarzschild Black Hole 1272

26.5 Spinning Black Holes: The Kerr Spacetime 1277

26.5.1 The Kerr Metric for a Spinning Black Hole 1277

26.5.2 Dragging of Inertial Frames 1279

26.5.3 The Light-Cone Structure, and the Horizon 1279

26.5.4 Evolution of Black Holes-Rotational Energy and Its Extraction 1282

26.6 The Many-Fingered Nature of Time 1293

Bibliographic Note 1297

27 Gravitational Waves and Experimental Tests of General Relativity 1299

27.1 Overview 1299

27.2 Experimental Tests of General Relativity 1300

27.2.1 Equivalence Principle, Gravitational Redshift, and Global Positioning System 1300

27.2.2 Perihelion Advance of Mercury 1302

27.2.3 Gravitational Deflection of Light, Fermat's Principle, and Gravitational Lenses 1305

27.2.4 Shapiro Time Delay 1308

27.2.5 Geodetic and Lense-Thirring Precession 1309

27.2.6 Gravitational Radiation Reaction 1310

27.3 Gravitational Waves Propagating through Flat Spacetime 1311

27.3.1 Weak, Plane Waves in Linearized Theory 1311

27.3.2 Measuring a Gravitational Wave by Its Tidal Forces 1315

27.3.3 Gravitons and Their Spin and Rest Mass 1319

27.4 Gravitational Waves Propagating through Curved Spacetime 1320

27.4.1 Gravitational Wave Equation in Curved Spacetime 1321

27.4.2 Geometric-Optics Propagation of Gravitational Waves 1322

27.4.3 Energy and Momentum in Gravitational Waves 1324

27.5 The Generation of Gravitational Waves 1327

27.5.1 Multipole-Moment Expansion 1328

27.5.2 Quadrupole-Moment Formalism 1330

27.5.3 Quadrupolar Wave Strength, Energy, Angular Momentum, and Radiation Reaction 1332

27.5.4 Gravitational Waves from a Binary Star System 1335

27.5.5 Gravitational Waves from Binaries Made of Black Holes, Neutron Stars, or Both: Numerical Relativity 1341

27.6 The Detection of Gravitational Waves 1345

27.6.1 Frequency Bands and Detection Techniques 1345

27.6.2 Gravitational-Wave Interferometers: Overview and Elementary Treatment 1347

27.6.3 Interferometer Analyzed in TT Gauge 1349

27.6.4 Interferometer Analyzed in the Proper Reference Frame of the Beam Splitter 1352

27.6.5 Realistic Interferometers 1355

27.6.6 Pulsar Timing Arrays 1355

Bibliographic Note 1358

28 Cosmology 1361

28.1 Overview 1361

28.2 General Relativistic Cosmology 1364

28.2.1 Isotropy and Homogeneity 1364

28.2.2 Geometry 1366

28.2.3 Kinematics 1373

28.2.4 Dynamics 1376

28.3 The Universe Today 1379

28.3.1 Baryons 1379

28.3.2 Dark Matter 1380

28.3.3 Photons 1381

28.3.4 Neutrinos 1382

28.3.5 Cosmological Constant 1382

28.3.6 Standard Cosmology 1383

28.4 Seven Ages of the Universe 1383

28.4.1 Particle Age 1384

28.4.2 Nuclear Age 1387

28.4.3 Photon Age 1392

28.4.4 Plasma Age 1393

28.4.5 Atomic Age 1397

28.4.6 Gravitational Age 1397

28.4.7 Cosmological Age 1400

28.5 Galaxy Formation 1401

28.5.1 Linear Perturbations 1401

28.5.2 Individual Constituents 1406

28.5.3 Solution of the Perturbation Equations 1410

28.5.4 Galaxies 1412

28.6 Cosmological Optics 1415

28.6.1 Cosmic Microwave Background 1415

28.6.2 Weak Gravitational Lensing 1422

28.6.3 Sunyaev-Zel'dovich Effect 1428

28.7 Three Mysteries 1431

28.7.1 Inflation and the Origin of the Universe 1431

28.7.2 Dark Matter and the Growth of Structure 1440

28.7.2 The Cosmological Constant and the Fate of the Universe 1444

Bibliographic Note 1447

App. A Special Relativity: Geometric Viewpoint 1449

2.1 Overview 1449

2.2 Foundational Concepts 1450

2.2.1 Inertial Frames, Inertial Coordinates, Events, Vectors, and Spacetime Diagrams 1450

2.2.2 The Principle of Relativity and Constancy of Light Speed 1454

2.2.3 The Interval and Its Invariance 1457

2.3 Tensor Algebra without a Coordinate System 1460

2.4 Particle Kinetics and Lorentz Force without a Reference Frame 1461

2.4.1 Relativistic Particle Kinetics: World Lines, 4-Velocity, 4-Momentum and Its Conservation, 4-Force 1461

2.4.2 Geometric Derivation of the Lorentz Force Law 1464

2.5 Component Representation of Tensor Algebra 1466

2.5.1 Lorentz Coordinates 1466

2.5.2 Index Gymnastics 1466

2.5.3 Slot-Naming Notation 1468

2.6 Particle Kinetics in Index Notation and in a Lorentz Frame 1469

2.7 Lorentz Transformations 1475

2.8 Spacetime Diagrams for Boosts 1477

2.9 Time Travel 1479

2.9.1 Measurement of Time; Twins Paradox 1479

2.9.2 Wormholes 1480

2.9.3 Wormhole as Time Machine 1481

2.10 Directional Derivatives, Gradients, and the Levi-Civita Tensor 1482

2.11 Nature of Electric and Magnetic Fields; Maxwell's Equations 1483

2.12 Volumes, Integration, and Conservation Laws 1487

2.12.1 Spacetime Volumes and Integration 1487

2.12.2 Conservation of Charge in Spacetime 1490

2.12.3 Conservation of Particles, Baryon Number, and Rest Mass 1491

2.13 Stress-Energy Tensor and Conservation of 4-Momentum 1494

2.13.1 Stress-Energy Tensor 1494

2.13.2 4-Momentum Conservation 1496

2.13.3 Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields 1497

Bibliographic Note 1500

References 1503

Name Index 1513

Subject Index 1515

Contents of the Unified Work, Modern Classical Physics 1527

Preface to Modem Classical Physics 1535

Acknowledgments for Modern Classical Physics 1543

What People are Saying About This

From the Publisher

“Extraordinarily impressive.”—Malcolm Longair, Nature

“A magnificent achievement.”—Edward Witten, Physics Today

Editorial Reviews

Kip S. Thorne, Co-Winner of the 2017 Nobel Prize in Physics

Roger D. Blandford, Co-Winner of the 2016 Crafoord Prize in Astronomy and Winner of the 2020 Shaw Prize in Astronomy

From the Publisher