Differential Geometry and General Relativity : Volume 1 / by Canbin Liang, Bin Zhou.

Format:

Book

Author/Creator:

Liang, Canbin.

Contributor:

Zhou, Bin.

Jia, Weizhen.

Series:

Graduate Texts in Physics, 1868-4521

Language:

English

Subjects (All):

Gravitation.

Geometry, Differential.

Mathematical physics.

Cosmology.

Classical and Quantum Gravity.

Differential Geometry.

Mathematical Methods in Physics.

Local Subjects:

Classical and Quantum Gravity.

Differential Geometry.

Mathematical Methods in Physics.

Cosmology.

Physical Description:

1 online resource (566 pages)

Edition:

1st ed. 2023.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2023.

Summary:

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.

Contents:

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 Einstein’s Equation

Schwarzschild Spacetimes

Cosmology

Appendix: The Conversion Between Systems of Geometrized and Nongeometrized Units.

Other Format:

Print version: Liang, Canbin Differential Geometry and General Relativity

ISBN:

981-9900-22-0