This book, the first in a three-volume set, explains general relativity using the mathematical tool of differential geometry. The book consists of ten chapters, the first five of which introduce differential geometry, which is widely applicable even outside the field of relativity. Chapter 6 analyzes special relativity using geometric language. In turn, the last four chapters introduce readers to the fundamentals of general relativity. Intended for beginners, this volume includes numerous exercises and worked-out example in each chapter to facilitate the learning experience. Chiefly written for graduate-level courses, the book’s content will also benefit upper-level undergraduate students, and can be used as a reference guide for practicing theoretical physicists.
Topological Spaces in Brief.- Manifolds and Tensor Fields.- The Riemann
(Intrinsic) Curvature Tensor.- Lie Derivative, Killing Fields and
Hypersurfaces.- Differential Forms and Their Integrals.- Special Relativity.-
Foundations of General Relativity.- Solving the Einsteins Equation.-
Schwarzschild Spacetimes.- Cosmology.- Appendix: The Conversion Between
Systems of Geometrized and Nongeometrized Units.
Canbin Liang (1938-2022) was a professor at Beijing Normal University, China. His main research area was general relativity. He received The First National Outstanding Teaching Achievement Award in 1989 and his book Electromagnetism was honored with the Excellent Textbook Award in 1988. He has published more than 50 research articles and 7 monographs.
Bin Zhou is an associate professor at Beijing Normal University, China. His research mainly focuses on general relativity and mathematical physics. He has published 27 research articles.
Weizhen Jia, the English translator of the book, is currently a PhD candidate at the University of Illinois at Urbana-Champaign, USA. He conducts research in the field of high energy physics.
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