Einstein gravity in a nutshell

Machine generated contents note: 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.Kaluza, 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.