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 CDM universe model. In addition an introduction to Noether s theorem within classical mechanics is added in Chapter 1.
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.
Reviews of the 1st Edition:"A sophisticated treatment of general relativity with a considerable number of applications to cosmology. ... The book may be read in several different ways, depending on the interests of readers. A rich source of material; college libraries should have it on their shelves. Summing Up: Highly recommended. Upper-division undergraduates through professionals." (K. L. Schick, CHOICE, Vol. v4 (3), November, 2007)"This book is a carefully prepared overview about all essential aspects of relativity. Its 5 parts give the standard way to present the material ... . Differently from other textbooks, the present authors emphasize much more concrete problems and examples ... . The book contains a very large number of formulas, partially due to the fact, that many statements are given both in the old index-notation as well as in the modern index-free notation; I think this is helpful for the readers." (Hans-Jürgen Schmidt, Zentralblatt MATH, Vol.
1126 (3), 2008)"Even if you already have a sizable collection of books on general relativity, or if you are looking for a good modern book to teach a course from, the text by Grøn and Hervik is ... a valuable addition to your collection." (David H. Delphenich, Mathematical Reviews, Issue 2008 i)
