This advanced undergraduate text introduces Einstein's general theory of relativity. The topics covered include geometric formulation of special relativity, the principle of equivalence, Einstein's field equation and its spherical-symmetric solution, as well as cosmology. An emphasis is placed on physical examples and simple applications without the full tensor apparatus. It begins by examining the physics of the equivalence principle and looks at how it inspired Einstein's idea of curved spacetime as the gravitational field. At a more mathematically accessible level, it provides a metric description of a warped space, allowing the reader to study many interesting phenomena such as gravitational time dilation, GPS operation, light deflection, precession of Mercury's perihelion, and black holes. Numerous modern topics in cosmology are discussed from primordial inflation and cosmic microwave background to the dark energy that propels an accelerating universe. Building on Cheng's previous book, 'Relativity, Gravitation and Cosmology: A Basic Introduction', this text has been tailored to the advanced student.
It concentrates on the core elements of the subject making it suitable for a one-semester course at the undergraduate level. It can also serve as an accessible introduction of general relativity and cosmology for those readers who want to study the subject on their own. The proper tensor formulation of Einstein's field equation is presented in an appendix chapter for those wishing to glimpse further at the mathematical details.
Ta-Pei Cheng is a particle physics theorist. After graduating from Dartmouth College, he obtained his PhD at Rockefeller University with the noted physicist and Einstein biographer Abraham Pais. During 1973-2007 he was on the faculty at University of Missouri - St. Louis, where he now holds the rank of Professor Emeritus. Starting the early 1980's Oxford University Press has published a number of his books, the most recent one being "Einstein's Physics: Atoms, Quanta, and Relativity - Derived, Explained, and Appraised".
1. Introduction ; 2. Special relativity: the new kinematics ; 3. Special relativity: the flat spacetime ; 4. Equivalence of gravitation and inertia ; 5. GR as a geometric theory of gravity ; 6. GR field equations and its spherical solution ; 7. Black holes ; 8. The GR framework for cosmology ; 9. Big bang thermal relics ; 10. Inflation and the accelerating universe ; 11. Tensors formalism for GR ; Appendix A: Answer keys to review questions ; Appendix B: Solution keys to selected exercises ; Appendix C: Glossary of symbols and acronyms ; References and bibliography