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.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: What Is Spacetime?
• Chapter 2: Mathematical Preliminaries: Sets, Maps, Topology, and Smooth Manifolds
• Chapter 3: The Geometry of Measurement: Metrics, Intervals, and Causal Structure
• Chapter 4: From Galilean Spacetime to Minkowski Spacetime
• Chapter 5: Special Relativity in Four-Dimensional Form
• Chapter 6: Fields on Minkowski Spacetime
• Chapter 7: Variational Principles and Spacetime Symmetries
• Chapter 8: Curved Spacetime: The Equivalence Principle
• Chapter 9: Covariant Differentiation, Parallel Transport, and Geodesics
• Chapter 10: Curvature and Its Physical Meaning
• Chapter 11: Einstein’s Field Equations
• Chapter 12: Exact Solutions and Their Spacetime Lessons
• Chapter 13: Black Holes, Horizons, and Global Structure
• Chapter 14: Cosmological Spacetime
• Chapter 15: Initial Value Formulation and the Dynamics of Geometry
• Chapter 16: Causality, Singularities, and Global Lorentzian Geometry
• Chapter 17: Spacetime and Quantum Field Theory
• Chapter 18: Quantum Fields in Curved Spacetime
• Chapter 19: Gauge Symmetry, Fiber Bundles, and Spacetime Structure
• Chapter 20: Effective Field Theory and the Search for Quantum Gravity
• Chapter 21: Candidate Foundations: Strings, Loops, Causal Sets, and Holography
• Chapter 22: The Reality and Emergence of Spacetime
• Conclusion