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

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. The most important additions in the second edition are included there. Anisotropic cosmological models are also included. The book contains many new exercises and examples, each with separate headings. Furthermore, detailed solutions of all the exercises are included except those in the advanced section.

List of contents

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.

About the author

Øyvind G. Grøn is a professor emeritus at the University of Oslo and Oslo Metropolitan University. His work mainly focuses on general relativity, gravitation and cosmology. He received his Candidatus realium from the Institute of Geophysics, the University of Oslo in 1973 and his Ph.D. from the Institute of Physics, University of Oslo in 1990. He was honored with the research prize of Illustrert Vitenskap and the King’s Gold Medal in 1988, the research prize of Oslo University College in 2004, the popularization prize of Oslo University College in 2009, and the Universe outstanding reviewer award in 2025. He has been a member of the Royal Norwegian Society of Sciences and Letters since 2005, an honorary member of the Norwegian Astronomical Society and of the Norwegian Physical Society since 2010 and 2023, respectively. He has served as an editorial board member of scientific journals—European Journal of Physics, Universe, Physica Scripta—and contributed to Fra Fysikkens Verden as an editor.

Sigbjørn Hervik is a professor at the Department of Applied Mathematics, the University of Stavanger. His work focuses on Riemannian geometry, Lorentzian geometry, Lie group and algebras, homogeneous spaces, relativity, cosmology from the mathematical aspects, alternative theory of gravity and classification issues for exact solutions in general relativity. He received his Ph.D. from Cambridge University in 2004. After his professional experience as a postdoc fellow at Dalhousie University in Canada, he was appointed to the current position in 2008. He has been teaching mathematics at all levels. He has received several research grants including a Toppforsk grant from the Research Council of Norway regarding interdisciplinary research between differential geometry and general relativity. He was honored with the Olav Thon prize for teaching excellence—a prestigious national teaching prize—in 2022.

Summary

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.

Additional text

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)

Report

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)

Product details

• Authors: Øyvind Grøn, Sigbjørn Hervik
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Release: 10.11.2025
• EAN: 9783032005588
• ISBN: 978-3-0-3200558-8
• No. of pages: 650
• Illustrations: Approx. 650 p. 200 illus., 50 illus. in color.
• Series: Graduate Texts in Physics
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Theoretical physics; Kosmologie und das Universum, Mathematische Physik, Cosmology, Mathematical Methods in Physics, Classical and Quantum Gravity, special theory of relativity, Einstein's field equations, Homogeneous and Isotropic Universe Models, Kaluza-Klein Theory, Introduction to General Relativity, Cosmological Principles, Canonical Cosmology, Non-inertial Reference Frames, Schwarzschild Solution and Black Holes, Covariant decomposition, Bianchi Models