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
5 - Einstein’s Field Equations
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
Einsteins field equations are derived and discussed. It is argued that the Einstein tensor is proportional to the energy-momentum tensor and the constant of proportionality is derived by demanding that Newton’s Universal Law of gravitation be recovered in the non-relativistic limit. The modification of Einstein's equations when a cosmological constant is introduced is also presented.
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- Einstein's General Theory of RelativityA Concise Introduction, pp. 119 - 125Publisher: Cambridge University PressPrint publication year: 2023