Informationen zum Autor Simon Sherwood is the author of Quantum Untangling (Wiley, 2023). Previously he was Chairman of Elegant Hotels PLC and the CEO of Orient-Express Hotels. He holds an MBA from Harvard Business School and is also a former strategy consultant with the Boston Consulting Group. Klappentext An easy-to-read introduction to Einstein's theory of general relativity In Untangling General Relativity, Simon Sherwood explains the details of general relativity with clarity, enthusiasm, and a sense of fun. Designed to be accessible to non-experts, the book combines intuitive explanations with the essential mathematics needed for a deep understanding of the subject. Sherwood introduces that maths gradually and clearly, in a step-by-step program designed to expand your appreciation and grasp of general relativity. Untangling General Relativity serves as an effective springboard for more in-depth studies. It lays the groundwork for mastering the advanced topics covered in relativity textbooks and university physics courses. Readers will find: A thorough introduction to general relativity, including the interpretation of gravity as curved spacetime and a full derivation of Einstein's field equationsComprehensive explanations of the spacetime metric, the equivalence principle, the geodesic equation, and the energy-momentum and curvature tensorsVacuum curvature: the Schwarzschild and Kerr metrics, black holes, white holes, event horizons, and gravitational wavesCosmology: the Friedmann equations, dark matter and energy, the Big Bang, inflation and an overview of current efforts to develop a quantum theory of gravity Perfect for undergraduate students preparing to take a university-level physics course dealing with general relativity for the first time, Untangling General Relativity will also benefit students of the natural sciences and instructors and educators with a professional or academic interest in the subject. Inhaltsverzeichnis Acknowledgements xii Introduction xiii Module I The Essentials 1 1 Overview 3 1.1 Einstein Field Equations 3 1.2 Gravity as Curved Spacetime 5 1.3 The Equivalence Principle 6 1.4 Working Out the Details 7 1.5 Gimme, Gimme, Gimme... Some Hard Evidence 7 1.6 The Cosmological Constant 8 1.7 Vacuum Curvature 8 1.8 Cosmology 9 1.9 The Field Equations in Full Form 11 2 Special Relativity 13 2.1 Relativity 13 2.2 The Speed of Light Is Constant: So What? 14 2.3 The Invariant Interval Equation 15 2.4 Time Dilation Quantified 16 2.5 Length Contraction 17 2.6 Leading Clocks Lag 18 2.7 Adding Things Up: An Apparent Paradox 19 2.8 Energy and Momentum 20 2.9 Energy, Momentum, Time and Space 21 2.10 Summary 22 3 The Metric 23 3.1 The Minkowski Metric 23 3.2 Einstein's Tensor and the Metric 25 3.3 Distortion in the Metric 25 3.4 Curvature, Dung Balls and a First Hint of Gravity 28 3.5 A Mathematical Challenge 29 3.6 Upper and Lower Indices 30 3.7 Raising/Lowering Indices with Wonky Metrics (Off-Diagonal Terms) 32 3.8 Summary 34 4 Covariant Derivatives and Christoffel Symbols 37 4.1 Covariant Derivatives 37 4.2 Christoffel Symbols 39 4.3 Summary 43 5 The Geodesic Equation and Gravity 45 5.1 A 2-D Model of Time Dilation and Gravitational Acceleration 45 5.2 The Geodesic Equation 46 5.3 What Happens to the Dung Beetle? 48 5.4 Albert Versus Isaac: Differences Emerge 49 5.5 Albert Versus Isaac: Seeing the Light 51 5.6 A Victory for Einstein 52 5.7 Time Dilation: Hafele-Keating and GPS 53 5.8 Geodesic Summary 54 5.9 Tensors: Why...? What...? How...? 55 5.10 Where's the Fridge? 55 6 The Equiva...

Autorentext

Simon Sherwood is the author of Quantum Untangling (Wiley, 2023). Previously he was Chairman of Elegant Hotels PLC and the CEO of Orient-Express Hotels. He holds an MBA from Harvard Business School and is also a former strategy consultant with the Boston Consulting Group.

Klappentext

An easy-to-read introduction to Einstein's theory of general relativity In Untangling General Relativity, Simon Sherwood explains the details of general relativity with clarity, enthusiasm, and a sense of fun. Designed to be accessible to non-experts, the book combines intuitive explanations with the essential mathematics needed for a deep understanding of the subject. Sherwood introduces that maths gradually and clearly, in a step-by-step program designed to expand your appreciation and grasp of general relativity. Untangling General Relativity serves as an effective springboard for more in-depth studies. It lays the groundwork for mastering the advanced topics covered in relativity textbooks and university physics courses. Readers will find:

• A thorough introduction to general relativity, including the interpretation of gravity as curved spacetime and a full derivation of Einstein's field equations
• Comprehensive explanations of the spacetime metric, the equivalence principle, the geodesic equation, and the energy-momentum and curvature tensors
• Vacuum curvature: the Schwarzschild and Kerr metrics, black holes, white holes, event horizons, and gravitational waves
• Cosmology: the Friedmann equations, dark matter and energy, the Big Bang, inflation and an overview of current efforts to develop a quantum theory of gravity Perfect for undergraduate students preparing to take a university-level physics course dealing with general relativity for the first time, Untangling General Relativity will also benefit students of the natural sciences and instructors and educators with a professional or academic interest in the subject.

Inhalt

Acknowledgements xii Introduction xiii

Module I The Essentials 1

1 Overview 3

1.1 Einstein Field Equations 3

1.2 Gravity as Curved Spacetime 5

1.3 The Equivalence Principle 6

1.4 Working Out the Details 7

1.5 Gimme, Gimme, Gimme... Some Hard Evidence 7

1.6 The Cosmological Constant 8

1.7 Vacuum Curvature 8

1.8 Cosmology 9

1.9 The Field Equations in Full Form 11

2 Special Relativity 13

2.1 Relativity 13

2.2 The Speed of Light Is Constant: So What? 14

2.3 The Invariant Interval Equation 15

2.4 Time Dilation Quantified 16

2.5 Length Contraction 17

2.6 Leading Clocks Lag 18

2.7 Adding Things Up: An Apparent Paradox 19

2.8 Energy and Momentum 20

2.9 Energy, Momentum, Time and Space 21

2.10 Summary 22

3 The Metric 23

3.1 The Minkowski Metric 23

3.2 Einstein's Tensor and the Metric 25

3.3 Distortion in the Metric 25

3.4 Curvature, Dung Balls and a First Hint of Gravity 28

3.5 A Mathematical Challenge 29

3.6 Upper and Lower Indices 30

3.7 Raising/Lowering Indices with Wonky Metrics (Off-Diagonal Terms) 32

3.8 Summary 34

4 Covariant Derivatives and Christoffel Symbols 37

4.1 Covariant Derivatives 37

4.2 Christoffel Symbols 39

4.3 Summary 43

5 The Geodesic Equation and Gravity 45

5.1 A 2-D Model of Time Dilation and Gravitational Acceleration 45

5.2 The Geodesic Equation 46

5.3 What Happens to the Dung Beetle? 48

5.4 Albert Versus Isaac: Differences Emerge 49

5.5 Albert Versus Isaac: Seeing the Light 51

5.6 A Victory for Einstein 52

5.7 Time Dilation: Hafele-Keating and GPS 53

5.8 Geodesic Summary 54

5.9 Tensors: Why...? What...? How...? 55

5.10 Where's the Fridge? 55

6 The Equivalence Principle and Ricci Tensor 57

6.1 The Equivalence Principle 57

6.2 From Newton's Gravity to Geodesic Separation 60

6.3 The Magnificent Ricci Tensor 62

6.4 An Intuitive Explanation of the Ricci Tensor 62

6.5 Vacuum Curvature: An Apparent Paradox 64

6.6 The Ricci Scalar 65

6.7 Summary 65

7 The Maths of Curvature 67

7.1 Parallel Transport 67

7.2 The Riemann Tensor 68

7.3 Calculating the Ricci Tensor 72

7.4 Calculating the Ricci Scalar 73

7.5 Example Calculations: Aarrgghh! 73

7.6 Hunting for Vacuum Solutions 76

7.7 Summary 77

8 The Energy-Momentum Tensor 79

8.1 Tensor Indices 79

8.2 Introduction to the Energy-Momentum Tensor 80

8.3 Mass Density Flow of Dust 81

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