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Table of contents
Spacetime from First Principles
A graduate path from geometry and relativity to curvature, fields, quantum structure, and the foundations of spacetime
Read each section in order. Every title can be opened as a TheoryTrace document.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: What Is Spacetime?5
- Chapter 2: Mathematical Preliminaries: Sets, Maps, Topology, and Smooth Manifolds6
- Chapter 3: The Geometry of Measurement: Metrics, Intervals, and Causal Structure7
- Chapter 4: From Galilean Spacetime to Minkowski Spacetime8
- Chapter 5: Special Relativity in Four-Dimensional Form9
- Chapter 6: Fields on Minkowski Spacetime10
- Chapter 7: Variational Principles and Spacetime Symmetries11
- Chapter 8: Curved Spacetime: The Equivalence Principle12
- Chapter 9: Covariant Differentiation, Parallel Transport, and Geodesics13
- Chapter 10: Curvature and Its Physical Meaning14
- Chapter 11: Einstein’s Field Equations15
- Chapter 12: Exact Solutions and Their Spacetime Lessons16
- Chapter 13: Black Holes, Horizons, and Global Structure17
- Chapter 14: Cosmological Spacetime18
- Chapter 15: Initial Value Formulation and the Dynamics of Geometry19
- Chapter 16: Causality, Singularities, and Global Lorentzian Geometry20
- Chapter 17: Spacetime and Quantum Field Theory21
- Chapter 18: Quantum Fields in Curved Spacetime22
- Chapter 19: Gauge Symmetry, Fiber Bundles, and Spacetime Structure23
- Chapter 20: Effective Field Theory and the Search for Quantum Gravity24
- Chapter 21: Candidate Foundations: Strings, Loops, Causal Sets, and Holography25
- Chapter 22: The Reality and Emergence of Spacetime26
- Conclusion27