An Introduction to General Relativity

Cambridge University Press

This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.

Autoren/Hrsg.

Hughston, L. P.

Tod, K. P.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhalt

Preface; 1. Introduction; 2. Vectors and tensors in flat three-space; 3. Aspects of special relativistic geometry; 4. Tensor analysis on manifolds; 5. Covariant differentiation; 6. Properties of the Riemann tensor; 7. Riemannian geometry; 8. The Lie derivative; 9. Geodesics; 10. Geodesic deviation; 11. Differential forms; 12. The transition from Newtonian theory; 13. Einstein's field equations; 14. The slow motion approximation; 15. The Schwarzschild solution; 16. Gravitational red-shift and time dilation; 17. The geodesic equation for the Schwarzschild solution; 18. Classical tests; 19. The extended Schwarzschild solution; 20. Black holes and gravitational collapse; 21. Interior solutions; 22. The Kerr solution; 23. Homogeneous and isotropic three-spaces; 24. Cosmology: kinematics; 25. Cosmology: dynamics; 25. Anisotropic cosmologies; Index.