This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere.
- Provides an accessible introduction to Einstein's general theory of relativity
- Guides readers from Newtonian mechanics to the frontiers of modern research
- Emphasizes symmetry and the Einstein-Hilbert action
- Covers topics not found in standard textbooks on Einstein gravity
- Includes interesting historical asides
- Features numerous exercises and detailed appendices
- Ideal for students, physicists, and scientifically minded lay readers
- Solutions manual (available only to teachers)
About the Author
A. Zee is professor of physics at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. His books include Quantum Field Theory in a Nutshell and Fearful Symmetry: The Search for Beauty in Modern Physics (both Princeton).
Table of Contents
Part 0: Setting the StagePrologue: Three Stories 3Introduction: A Natural System of Units, the Cube of Physics, Being Overweight, & Hawking Radiation 10Prelude: Relativity Is an Everyday and Ancient Concept 17ONE Book One: From Newton to the Gravitational RedshiftI Part I: From Newton to Riemann: Coordinates to CurvatureI.1 Newton's Laws 25I.2 Conservation Is Good 35I.3 Rotation: Invariance and Infinitesimal Transformation 38I.4 Who Is Afraid of Tensors? 52I.5 From Change of Coordinates to Curved Spaces 62I.6 Curved Spaces: Gauss and Riemann 82I.7 Differential Geometry Made Easy, but Not Any Easier! 96Recap to Part I 110II Part II: Action, Symmetry, and ConservationII.1 The Hanging String and Variational Calculus 113II.2 The Shortest Distance between Two Points 123II.3 Physics Is Where the Action Is 136II.4 Symmetry and Conservation 150Recap to Part II 155III Part III: Space and Time UnifiedIII.1 Galileo versus Maxwell 159III.2 Einstein's Clock and Lorentz's Transformation 166III.3 Minkowski and the Geometry of Spacetime 174III.4 Special Relativity Applied 195III.5 The Worldline Action and the Unification of Material Particles with Light 207III.6 Completion, Promotion, and the Nature of the Gravitational Field 218Recap to Part III 238IV Part IV: Electromagnetism and GravityIV.1 You Discover Electromagnetism and Gravity! 241IV.2 Electromagnetism Goes Live 248IV.3 Gravity Emerges! 257Recap to Part IV 261TWO Book Two: From the Happiest Thought to the UniversePrologue to Book Two: The Happiest Thought 265V Part V: Equivalence Principle and Curved SpacetimeV.1 Spacetime Becomes Curved 275V.2 The Power of the Equivalence Principle 280V.3 The Universe as a Curved Spacetime 288V.4 Motion in Curved Spacetime 301V.5 Tensors in General Relativity 312V.6 Covariant Differentiation 320Recap to Part V 334VI Part VI: Einstein's Field Equation Derived and Put to WorkVI.1 To Einstein's Field Equation as Quickly as Possible 337VI.2 To Cosmology as Quickly as Possible 355VI.3 The Schwarzschild-Droste Metric and Solar System Tests of Einstein Gravity 362VI.4 Energy Momentum Distribution Tells Spacetime How to Curve 378VI.5 Gravity Goes Live 388VI.6 Initial Value Problems and Numerical Relativity 400Recap to Part VI 406VII Part VII: Black HolesVII.1 Particles and Light around a Black Hole 409VII.2 Black Holes and the Causal Structure of Spacetime 419VII.3 Hawking Radiation 436VII.4 Relativistic Stellar Interiors 451VII.5 Rotating Black Holes 458VII.6 Charged Black Holes 477Recap to Part VII 485VIII Part VIII: Introduction to Our UniverseVIII.1 The Dynamic Universe 489VIII.2 Cosmic Struggle between Dark Matter and Dark Energy 502VIII.3 The Gamow Principle and a Concise History of the Early Universe 515VIII.4 Inflationary Cosmology 530Recap to Part VIII 537THREE Book Three: Gravity at Work and at PlayIX Part IX: Aspects of GravityIX.1 Parallel Transport 543IX.2 Precession of Gyroscopes 549IX.3 Geodesic Deviation 552IX.4 Linearized Gravity, Gravitational Waves, and the Angular Momentum of Rotating Bodies 563IX.5 A Road Less Traveled 578IX.6 Isometry, Killing Vector Fields, and Maximally Symmetric Spaces 585IX.7 Differential Forms and Vielbein 594IX.8 Differential Forms Applied 607IX.9 Conformal Algebra 614IX.10 De Sitter Spacetime 624IX.11 Anti de Sitter Spacetime 649Recap to Part IX 668X Part X: Gravity Past, Present, and FutureX.1 Kałuza, Klein, and the Flowering of Higher Dimensions 671X.2 Brane Worlds and Large Extra Dimensions 696X.3 Effective Field Theory Approach to Einstein Gravity 708X.4 Finite Sized Objects and Tidal Forces in Einstein Gravity 714X.5 Topological Field Theory 719X.6 A Brief Introduction to Twistors 729X.7 The Cosmological Constant Paradox 745X.8 Heuristic Thoughts about Quantum Gravity 760Recap to Part X 775Closing Words 777Timeline of Some of the People Mentioned 791Solutions to Selected Exercises 793Bibliography 819Index 821Collection of Formulas and Conventions 859