Relativity, Gravitation and Cosmology

Einstein’s general theory of relativity is introduced in this advanced undergraduate and beginning graduate level textbook. Topics include special relativity, in the formalism of Minkowski’s four-dimensional space-time, the principle of equivalence, Riemannian geometry and tensor analysis, Einstein field equation, as well as many modern cosmological subjects, from primordial inflation and cosmic microwave anisotropy to the dark energy that propels an accelerating universe.

The author presents the subject with an emphasis on physical examples and simple applications without the full tensor apparatus. The reader first learns how to describe curved spacetime. At this mathematically more accessible level, the reader can already study the many interesting phenomena such as gravitational lensing, precession of Mercury’s perihelion, black holes, and cosmology. The full tensor formulation is presented later, when the Einstein equation is solved for a few symmetric cases. Many modern topics in cosmology are discussed in this book: from inflation, cosmic microwave anisotropy to the “dark energy” that propels an accelerating universe.

Mathematical accessibility, together with the various pedagogical devices (e.g., worked-out solutions of chapter-end problems), make it practical for interested readers to use the book to study general relativity and cosmology on their own.

Table of Contents

PART I: PRELIMINARIES

1 Introduction and overview

2 Special relativity: The basics

PART II: RELATIVITY: METRIC DESCRIPTION OF SPACETIME

3 Special relativity: The geometric formulation

4 The principle of equivalence

5 Metric description of a curved space

6 GR as a geometric theory of gravity – I

7 Spherically symmetric spacetime – GR tests 8 Black holes

PART III: COSMOLOGY

9 The homogeneous and isotropic universe

10 The expanding universe and thermal relics

11 Inflation and the accelerating universe

PART IV: RELATIVITY: FULL TENSOR FORMULATION

12 Tensors in special relativity

13 Tensors in general relativity

14 GR as a geometric theory of gravity – II

15 Linearized theory and gravitational waves PART V: ENDNOTES

• Answer keys to review questions

• Solutions to selected problems

• Glossary of symbols and acronyms

• References and bibliography

• Physical constants

Review

The book “… is perhaps a bit modest in its title: Comprehensive rather than Basic is probably more appropriate. This second edition expands upon the 2005 textbook, which is a ‘Physics First’ presentation of relativity and cosmology.” — Journal of General Relativity & Gravitation (2011) 43:359-360.

Book Description

A “physics-first” introduction to Einstein’s general theory of relativity

About the Author

Ta-Pei Cheng is currently Emeritus Professor of Physics at the University of Missouri – St. Louis. He took his Ph.D. at Rockefeller University in 1969, followed by post-doctoral study at Rockefeller University and at the Institute for Advanced Study (Princeton). He has been on the faculty of University of Missouri – St. Louis from 1973 to the present day, and was elected a Fellow of the American Physical Society in 1982.