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)

#### Awards and Recognition

- One of Choice's Outstanding Academic Titles for 2013

**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).

- Preface
- 0 Part o: Setting the Stage
- Prologue: Three Stories
- Introduction: A Natural System of Units, the Cube of Physics, Being Overweight, and Hawking Radiation
- Prelude: Relativity Is an Everyday and Ancient Concept

- ONE Book One: From Newton to the Gravitational Redshift
- I Part I: From Newton to Riemann: Coordinates to Curvature
- I.1 Newton’s Laws
- I.2 Conservation Is Good
- I.3 Rotation: Invariance and Infinitesimal Transformation
- I.4 Who Is Afraid of Tensors?
- I.5 From Change of Coordinates to Curved Spaces
- I.6 Curved Spaces: Gauss and Riemann
- I.7 Differential Geometry Made Easy, but Not Any Easier!
- Recap to Part I

- II Part II: Action, Symmetry, and Conservation
- II.1 The Hanging String and Variational Calculus
- II.2 The Shortest Distance between Two Points
- II.3 Physics Is Where the Action Is
- II.4 Symmetry and Conservation
- Recap to Part II

- III Part III: Space and Time Unified
- III.1 Galileo versus Maxwell
- III.2 Einstein’s Clock and Lorentz’s Transformation
- III.3 Minkowski and the Geometry of Spacetime
- III.4 Special Relativity Applied
- III.5 The Worldline Action and the Unification of Material Particles with Light
- III.6 Completion, Promotion, and the Nature of the Gravitational Field
- Recap to Part III

- IV Part IV: Electromagnetism and Gravity
- IV.1 You Discover Electromagnetism and Gravity!
- IV.2 Electromagnetism Goes Live
- IV.3 Gravity Emerges!
- Recap to Part IV

- TWO Book Two: From the Happiest Thought to the Universe
- Prologue to Book Two: The Happiest Thought
- V Part V: Equivalence Principle and Curved Spacetime
- V.1 Spacetime Becomes Curved
- V.2 The Power of the Equivalence Principle
- V.3 The Universe as a Curved Spacetime
- V.4 Motion in Curved Spacetime
- V.5 Tensors in General Relativity
- V.6 Covariant Differentiation
- Recap to Part V

- VI Part VI: Einstein’s Field Equation Derived and Put to Work
- VI.1 To Einstein’s Field Equation as Quickly as Possible
- VI.2 To Cosmology as Quickly as Possible
- VI.3 The Schwarzschild-Droste Metric and Solar System Tests of Einstein Gravity
- VI.4 Energy Momentum Distribution Tells Spacetime How to Curve
- VI.5 Gravity Goes Live
- VI.6 Initial Value Problems and Numerical Relativity
- Recap to Part VI

- VII Part VII: Black Holes
- VII.1 Particles and Light around a Black Hole
- VII.2 Black Holes and the Causal Structure of Spacetime
- VII.3 Hawking Radiation
- VII.4 Relativistic Stellar Interiors
- VII.5 Rotating Black Holes
- VII.6 Charged Black Holes
- Recap to Part VII

- VIII Part VIII: Introduction to Our Universe
- VIII.1 The Dynamic Universe
- VIII.2 Cosmic Struggle between Dark Matter and Dark Energy
- VIII.3 The Gamow Principle and a Concise History of the Early Universe
- VIII.4 Inflationary Cosmology
- Recap to Part VIII

- THREE Book Three: Gravity at Work and at Play
- IX Part IX: Aspects of Gravity
- IX.1 Parallel Transport
- IX.2 Precession of Gyroscopes
- IX.3 Geodesic Deviation
- IX.4 Linearized Gravity, Gravitational Waves, and the Angular Momentum of Rotating Bodies
- IX.5 A Road Less Traveled
- IX.6 Isometry, Killing Vector Fields, and Maximally Symmetric Spaces
- IX.7 Differential Forms and Vielbein
- IX.8 Differential Forms Applied
- IX.9 Conformal Algebra
- IX.10 De Sitter Spacetime
- IX.11 Anti de Sitter Spacetime
- Recap to Part IX

- X Part X: Gravity Past, Present, and Future
- X.1 Kałuza, Klein, and the Flowering of Higher Dimensions
- X.2 Brane Worlds and Large Extra Dimensions
- X.3 Effective Field Theory Approach to Einstein Gravity
- X.4 Finite Sized Objects and Tidal Forces in Einstein Gravity
- X.5 Topological Field Theory
- X.6 A Brief Introduction to Twistors
- X.7 The Cosmological Constant Paradox
- X.8 Heuristic Thoughts about Quantum Gravity
- Recap to Part X

- Closing Words
- Timeline of Some of the People Mentioned
- Solutions to Selected Exercises
- Bibliography
- Index
- Collection of Formulas and Conventions

"Zee writes in an informal, conversational style, displaying his extensive experience and close contacts with many undergraduate and graduate students."**—***Choice*

"*Einstein Gravity in a Nutshell* is a remarkably complete and thorough textbook on general relativity, written in a refreshing and engaging style. Zee leads us through all the major intellectual steps that make what is surely one of the most profound and beautiful theories of all time. The book is enjoyable and informative in equal measure. Quite an achievement."—Pedro Ferreira, University of Oxford

"Zee's new text on gravitation provides a wonderful introduction to Einstein's theory. Written at a level accessible to undergraduates, it prepares its readers for work at the research frontier, gently leading the reader to a modern and sophisticated understanding of the subject with a humorous, often conversational style. Providing broad coverage of the subject, including cosmology and black holes, it is an excellent complement to Hartle's book and good preparation for Carroll's."—Michael Dine, University of California, Santa Cruz

"*Einstein Gravity in a Nutshell* is richly infused with the author's wit and wisdom, with a refreshing emphasis on concepts rather than mathematics. Zee's writing is characteristically insightful, humorous, irreverent, and accessible."—Andrew Hamilton, University of Colorado, Boulder