Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Metrics
- 3 Geodesics
- 4 The Geometry of Curved Spaces
- 5 Einstein’s Field Equations
- 6 Solutions of Einstein’s Equations in Empty Space
- 7 Cosmology and the Big Bang
- Appendix A Tensors of Type (p, q)
- Appendix B The Riemann Tensor
- Appendix C The Energy-Momentum Tensor
- Appendix D The Schwarzschild Metric
- Appendix E Robertson-Walker Space-Time
- References
- Index
3 - Geodesics
Published online by Cambridge University Press: 15 June 2023
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Introduction
- 2 Metrics
- 3 Geodesics
- 4 The Geometry of Curved Spaces
- 5 Einstein’s Field Equations
- 6 Solutions of Einstein’s Equations in Empty Space
- 7 Cosmology and the Big Bang
- Appendix A Tensors of Type (p, q)
- Appendix B The Riemann Tensor
- Appendix C The Energy-Momentum Tensor
- Appendix D The Schwarzschild Metric
- Appendix E Robertson-Walker Space-Time
- References
- Index
Summary
Geodesics are introduced and the geodesic equation analysed for the geometries introduced in chapter 2, using variation principles of classical mechanics. Geodesic motino on a sphere is described as well as the Coriolis effect and the Sagnac effect. Newtonian gravity is derived as the non-relativistic limit of geodesic motion in space-time. Geodesics in an expanding universe and heat death is described. Geodesics in Schwarzschild space-time are treated in detail: the precession of the perihelion of Mercury; the bending of light by the Sun; Shapiro time delay; black holes and the event horizon. Gravitational waves and gravitational lensing are also covered.
Keywords
- Type
- Chapter
- Information
- Einstein's General Theory of RelativityA Concise Introduction, pp. 44 - 84Publisher: Cambridge University PressPrint publication year: 2023