02672nam 2200505 450 991071741690332120230613130057.09783031161391(electronic bk.)978303116138410.1007/978-3-031-16139-1(MiAaPQ)EBC7239633(Au-PeEL)EBL7239633(DE-He213)978-3-031-16139-1(OCoLC)1377309738(PPN)269656634(EXLCZ)992650625530004120230613h20182023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe geometry of spacetime a mathematical introduction to relativity theory /Rainer Oloff1st ed. 2023.Cham, Switzerland :Springer Spektrum,[2018]©20231 online resource (283 pages)Graduate Texts in Physics,1868-4521Print version: Oloff, Rainer The Geometry of Spacetime Cham : Springer International Publishing AG,c2023 9783031161384 Includes bibliographical references and index.Differentiable manifolds -- Tangent vectors -- Tensors -- Semi-Riemann manifolds -- Special relativity -- Differential forms -- Covariant derivation of vector fields -- Curvature -- Matter -- Geodesy -- Covariant differentiation of tensor fields -- Lie derivation -- Integration on manifolds -- Non-rotating black holes -- Cosmology -- Rotating black holes -- An overview of string theory.This book systematically develops the mathematical foundations of the theory of relativity and links them to physical relations. For this purpose, differential geometry on manifolds is introduced first, including differentiation and integration, and special relativity is presented as tensor calculus on tangential spaces. Using Einstein's field equations relating curvature to matter, the relativistic effects in the solar system including black holes are discussed in detail. The text is aimed at students of physics and mathematics and assumes only basic knowledge of classical differential and integral calculus and linear algebra.Graduate Texts in Physics,1868-4521Geometry, DifferentialRelativity (Physics)MathematicsGeometry, Differential.Relativity (Physics)Mathematics.516.36Oloff Rainer1226203MiAaPQMiAaPQMiAaPQ9910717416903321The Geometry of Spacetime3294450UNINA