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Spacetime.- What is Curvature?.- General Relativity Basics.- Spherically Symmetric Gravitational Field.- Geometry.- Vectors and Tensors.- Inner Product.- Elementary Differential Geometry.- Connection and Curvature.- Riemannian Geometry.- Additional Topics in Geometry.- Gravitation.- The Einstein Equation.- General Features of Spacetime.- Weak Gravitational Fields.- Schwarzschild and Kerr Solutions.- Cosmology.- Special Topics.
"This book meets my teaching needs, as it presents a very solid foundation for students who seek a comprehensive introduction into the difficult field of the general theory of relativity. The mathematical background is treated in a rigorous and nevertheless understandable style. Those readers who are novices in the field will welcome the fact that the author provides an abundance of carefully selected exercises together with their solutions. In summary, I will recommend this valuable textbook to my students and use it as the main text for my lectures." - Prof. Dr. P. Wirtz, Faculty of Computer Science and Mathematics, Hochschule Hegensburg, Germany
From the reviews: "The book is structured into three parts. The first part ! offers preliminary topics on general relativity. ! The second part is a comprehensive and accurate incursion in the mathematical background of relativity theory. ! The last part, entitled Gravitation, contains six chapters dealing with the Einstein equation ! cosmology and special topics. Interesting exercises with complete answers simplify the understanding of the presented material. The textbook is recommended to advanced graduates and researchers." (Ferenc Szenkovits, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010) "This book provides the reader with a very gentle introduction to the main ideas and concepts of general relativity. This work is particularly suitable for students who are interested in general relativity or are beginning to study this subject. Moreover, the author presents the reader with a number of problems and provides worked-out solutions, which will surely help the reader to obtain a deeper of interest to students who seek a smooth introduction to general relativity." (Guglielmo Fucci, Mathematical Reviews, Issue 2011 m)