Einstein's General Theory of Relativity

With Modern Applications in Cosmology

Øyvind Grøn, Sigbjorn Hervik, Sigbjorn Hervik

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English

Springer-Verlag New York Inc.
10 October 2010

Mathematics & Sciences; Mathematics; Gravity; Mathematical physics

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.

By: Øyvind Grøn, Sigbjorn Hervik, Sigbjorn Hervik
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 1st ed. Softcover of orig. ed. 2007
Dimensions: Height: 235mm, Width: 155mm, Spine: 28mm
Weight: 848g
ISBN: 9781441924063
ISBN 10: 144192406X
Pages: 558
Publication Date: 10 October 2010
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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).

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

From the reviews: 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-Jurgen 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 Gron and Hervik is ... a valuable addition to your collection. (David H. Delphenich, Mathematical Reviews, Issue 2008 i)