02818nam 2200505z- 450 991055784020332120231214133046.0(CKB)5580000000300707(oapen)https://directory.doabooks.org/handle/20.500.12854/80568(EXLCZ)99558000000030070720202204d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierFoundations of General RelativityFrom Einstein to Black HolesNijmegenRadboud University Press20211 electronic resource (394 pages)90-831789-2-7 This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.Foundations of General RelativityRiemannian geometryDifferential geometryRelativity physicsHistoryMathematicsTopologyMathematical physicsPenroseGravityEinsteinBlack holesMathematical RelativityRiemannian geometry.Differential geometry.Relativity physicsHistory.Mathematics.Topology.Landsman Klaasauth821832BOOK9910557840203321Foundations of General Relativity3032292UNINA