Noether Symmetries in Theories of Gravity : With Applications to Astrophysics and Cosmology (Cambridge Monographs on Mathematical Physics)

Bajardi, Francesco/ Capozziello, Salvatore

Cambridge University Press（2022/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 475 p.
• 言語 ENG
• 商品コード 9781009208741
• DDC分類 530.11

Full Description

This volume summarizes the many alternatives and extensions to Einstein's General Theory of Relativity, and shows how symmetry principles can be applied to identify physically viable models. The first part of the book establishes the foundations of classical field theory, providing an introduction to symmetry groups and the Noether theorems. A quick overview of general relativity is provided, including discussion of its successes and shortcomings, then several theories of gravity are presented and their main features are summarized. In the second part, the 'Noether Symmetry Approach' is applied to theories of gravity to identify those which contain symmetries. In the third part of the book these selected models are tested through comparison with the latest experiments and observations. This constrains the free parameters in the selected models to fit the current data, demonstrating a useful approach that will allow researchers to construct and constrain modified gravity models for further applications.

Contents

Preface; Acknowledgements; Amalie Emmy Noether: a life for mathematics; Notation; Acronyms; Part I. Preliminaries: 1. The concept of symmetry; 2. The two Noether theorems; 3. Applications of the Noether first theorem to fields and particles; 4. Theories of gravity: an overview; Part II. The Noether Symmetry Approach: 5. From the Noether theorem to the Noether symmetry approach; 6. The extensions of GR, TEGR and STEGR; 7. Higher-order extensions with the Gauss-Bonnet invariant; 8. Extensions with higher derivatives or R and T; 9. Scalar-tensor theories of gravity; 10. Non-local gravity; 11. Noether symmetries in Bianchi universes; 12. The Noether approach in spherical symmetry; Part III. Applications: 13. Applications to solar system, stars and our galaxy; 14. Applications to galaxies; 15. Applications to cosmology; 16. Applications to quantum cosmology; 17. Strings, swampland, renormalizability and viability; Epilogue; Appendices; References; Index.