Cheng T.-P. Relativity, Gravitation, and Cosmology: A basic introduction

Oxford: Oxford University Press. – 2005. – 354 p. It seems a reasonable expectation that every student receiving a university degree in physics will have had a course in one of the most important developments in modern physics: Einstein’s general theory of relativity. Also, given the exciting discoveries in astrophysics and cosmology of recent years, it is highly desirable to have an introductory course whereby such subjects can be presented in their proper framework. Again, this is general relativity (GR). Students should have had the usual math preparation at the calculus level, plus some familiarity with matrices, and the physics preparation of courses on mechanics and on electromagnetism where differential equations of Maxwell’s theory are presented. Some exposure to special relativity as part of an introductory modern physics course will also be helpful, even though no prior knowledge of special relativity will be assumed. Part I of this book concentrates on the metric description of spacetime: first, the flat geometry as in special relativity, and then curved ones for general relativity. Part II contains three chapters on cosmology. The tensor formulation of relativity is introduced in Part III. After presenting special relativity in a manifestly covariant formalism, we discuss covariant differentiation, parallel transport, and curvature tensor for a curved space. The subject of gravitational waves can be found in the concluding chapter.Relativity: Metric Description of Spacetime
Introduction and overview
Special relativity and the flat spacetime
The principle of equivalence
Metric description of a curved space
GR as a geometric theory of gravity - I
Spacetime outside a spherical star
Cosmology
The homogeneous and isotropic universe
The expanding universe and thermal relics
Inflation and the accelerating universe
Relativity: Full Tensor Formulation
Tensors in special relativity
Tensors in general relativity
GR as a geometric theory of gravity - II
Linearized theory and gravitational waves
The twin paradox
A glimpse of advanced topics in black hole physics
False vacuum and hidden symmetry
The problem of quantum vacuum energy
Answer keys to review questions
Solutions of selected problems