Titlebook: General Relativity; Norbert Straumann Textbook 2013Latest edition Springer Science+Business Media Dordrecht 2013 Einstein’s Field Equation

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https://doi.org/10.1007/978-3-319-31906-3 repeating some algebraic preliminaries on exterior algebras. Then exterior differential forms and the associated exterior algebra are introduced. On this we study general properties of derivations and antiderivations. The most important one is Cartan’s exterior derivative. Poincaré’s Lemma is also

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Małgorzata Stefania Lewandowska PhDivative” which transforms tensor fields into other tensor fields. This allows us to introduce many important notions, such as the parallel transport of tensor fields along a curve, geodesics, exponential mappings in the neighborhood of points, normal coordinates, and—most importantly—the concepts of

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Norbert StraumannProvides a complete revision and extension of the first edition.General Relativity and Relativistic Astrophysics’ with a whole new chapter on cosmology.The book provides a comprehensive and timely int

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978-94-007-9954-7Springer Science+Business Media Dordrecht 2013

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https://doi.org/10.1007/978-94-017-0355-0e a broad outline of general relativity (GR) as a profound theory of gravitation, and of its major applications and successes. It is now widely recognized that GR is a non-Abelian gauge theory of a special type, in that it has a common geometrical structure with the gauge theories of particle physics.

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Introductione a broad outline of general relativity (GR) as a profound theory of gravitation, and of its major applications and successes. It is now widely recognized that GR is a non-Abelian gauge theory of a special type, in that it has a common geometrical structure with the gauge theories of particle physics.

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Some Details and Supplementslong maps and their induced covariant derivatives, because this is used at various places in the book. For a convenient formulation we introduce the tangent bundle of a manifold, the prototype of a vector bundle. Applications to variations of curves will illustrate the usefulness of the concepts.