Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- 1 Aspects of Differential Geometry
- 2 Metric and Related Formulations
- 3 Cartan’s Tetrad Formulation
- 4 General Relativity in 2+1 Dimensions
- 5 The ‘Chiral’ Formulation of General Relativity
- 6 Chiral Pure Connection Formulation
- 7 Deformations of General Relativity
- 8 Perturbative Descriptions of Gravity
- 9 Higher-Dimensional Descriptions
- 10 Concluding Remarks
- References
- Index
Introduction
Published online by Cambridge University Press: 06 November 2020
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Introduction
- 1 Aspects of Differential Geometry
- 2 Metric and Related Formulations
- 3 Cartan’s Tetrad Formulation
- 4 General Relativity in 2+1 Dimensions
- 5 The ‘Chiral’ Formulation of General Relativity
- 6 Chiral Pure Connection Formulation
- 7 Deformations of General Relativity
- 8 Perturbative Descriptions of Gravity
- 9 Higher-Dimensional Descriptions
- 10 Concluding Remarks
- References
- Index
Summary
Historical introduction into the topic of formulations of General Relativity with their associated mathematical formalisms. We review the history of the idea that gravity is geometry, as well as the history of development of main geometical ideas of modern differential geometry. We start with metric geometry of Riemann, Levi and Civita, and describe the main contributions of Cartan. We touch upon the fact that spinors and differential forms are closely related, first observed by Chevalley. We give arguments for why formalisms based on differential forms may be superrior to the metric one.
- Type
- Chapter
- Information
- Formulations of General RelativityGravity, Spinors and Differential Forms, pp. 1 - 7Publisher: Cambridge University PressPrint publication year: 2020