Liang C., Zhou B. Differential Geometry and General Relativity: Volume 1

Springer, 2023. - 565 p. - (Graduate Texts in Physics). - ISBN 9819900212.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.Foreword.
Preface to the English Edition.
Preface to the Second Edition.
Preface to the First Edition.
Topological Spaces in Brief.
Manifolds and Tensor Fields.
The Riemann (Intrinsic) Curvature Tensor.
Lie Derivatives, Killing Fields and Hypersurfaces.
Differential Forms and Their Integrals.
Special Relativity.
Foundations of General Relativity.
Solving Einstein’s Equation.
Schwarzschild Spacetimes.
Cosmology I.
Appendix A: The Conversion Between Geometrized and Nongeometrized Unit Systems.
Conventions and Notation.
Index.True PDF