Einstein's General Theory of Relativity by Grà ̧n, à ̃yvind; Hervik, Sigbjà ̧rn;

Hosszú leírás:

"

This book is the second edition of the well-received textbook on the theory of general relativity by Øyvind G. Grøn and Sigbjørn Hervik. It introduces the general theory of relativity and includes applications to cosmology. The reader is given an updated introduction to general relativity including the most recent developments in cosmology. The book contains a thorough introduction to tensor calculus and curved manifolds.

After the necessary mathematical tools are introduced, the book provides a thorough presentation of the theory of relativity including a chapter on gravitational waves. This revised edition also contains detailed solutions to all the exercises in the first thirteen chapters for fundamental material, up to the remaining chapters devoted to advanced topics. The most important additions in the second edition are included there. The section on anisotropic cosmological models is expanded and updated, presenting an anisotropic generalization of our present standard model of the universe—the ΛCDM universe model. In addition an introduction to Noether’s theorem within classical mechanics is added in Chapter 1.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.

Tartalomjegyzék:

Relativity Principles and Gravitation.- The Special Theory of Relativity.- Vectors, Tensors, and Forms.- Basis Vector Fields and the Metric Tensor.- Non-inertial Reference Frames.- Differentiation, Connections, and Integration.- Curvature.- Einstein’s Field Equations.- The Linear Field Approximation.- The Schwarzschild Solution and Black Holes.- Homogeneous and Isotropic Universe Models.- Universe Models with Vacuum Energy.- Anisotropic and Inhomogeneous Universe Models.- Covariant Decomposition, Singularities, and Canonical Cosmology.- Spatially Homogeneous Universe Models.- Israel’s Formalism: The Metric Junction Method.- Brane-worlds.- Kaluza-Klein Theory.