Einstein's General Theory of Relativity: With Modern Applications in Cosmology

by Øyvind Grøn, Sigbjorn Hervik

Overview

The book introduces the general theory of relativity and includes applications to cosmology. The book contains a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, we give a thorough presentation of the theory of relativity. Also, some advanced topics not previously covered by textbooks; e.g. 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 get an updated introduction to general relativity including the most recent developments in cosmology.

Product Details

ISBN-13:	9780387691992
Publisher:	Springer New York
Publication date:	05/04/2007
Edition description:	2007
Pages:	538
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

About the Author

Both authors are researchers in general relativity with particular emphasis on cosmology. They have earned the following honors: Illustrert Vitenskaps research prize (1988), The King's Gold Medal (1990), 2nd prize, Smith-Knight Rayleight-Knight prizes, Cambridge University (2003), and Research Prize of Oslo College of Engineering (2004).

Table of Contents

Introduction: Newtonian Physics And Special Relativity.- Relativity Principles and Gravitation.- The Special Theory of Relativity.- The Mathematics Of The General 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.- Einstein's Field Equations.- The Linear Field Approximation.- The Schwarzschild Solution and Black Holes.- Cosmology.- Homogeneous and Isotropic Universe Models.- Universe Models with Vacuum Energy.- Anisotropic and Inhomogeneous Universe Models.- Advanced Topics.- Covariant Decomposition, Singularities, and Canonical Cosmology.- Spatially Homogeneous Universe Models.- Israel's Formalism: The Metric Junction Method.- Brane-worlds.- Kaluza-Klein Theory.

Editorial Reviews

Reviews of the 1^st 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)

From the Publisher