Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part IRelativity and Geometry
- 1Electromagnetism and Special Relativity
- 2Particle Motion under Relativistic Gravity
- 3Calculus on Manifolds
- 4Riemannian Geometry
- 5Maurer–Cartan
- Part IIGeneral Relativity
- Part IIICanonical Field Theories with Gravity
- Appendix: Fiber Bundles
- Index
2 - Particle Motion under Relativistic Gravity
from Part I - Relativity and Geometry
Published online by Cambridge University Press: 01 March 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part IRelativity and Geometry
- 1Electromagnetism and Special Relativity
- 2Particle Motion under Relativistic Gravity
- 3Calculus on Manifolds
- 4Riemannian Geometry
- 5Maurer–Cartan
- Part IIGeneral Relativity
- Part IIICanonical Field Theories with Gravity
- Appendix: Fiber Bundles
- Index
Summary
Once the proper time is recognized as the only viable notion of time, relativistic gravity as an external force arises naturally via the analogy of how one introduces the metric in Newtonian dynamics in curvilinear coordinates. The resulting action principle comes with a key property that the time parameter choice should be entirely irrelevant to the dynamics, which is, in turn, used to simplify the action by choosing the parameter to be the proper time of the particle in question. With the metric supplied later by the gravitational field equation, we discover that the Kepler problem elevates to a fully relativistic one straightforwardly. This chapter closes with the application of all these to the light-bending phenomena.
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- Chapter
- Information
- Gravitation for Theorists , pp. 18 - 28Publisher: Cambridge University PressPrint publication year: 2026
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