LEADER 02818nam 2200505z- 450 001 9910557840203321 005 20231214133046.0 035 $a(CKB)5580000000300707 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/80568 035 $a(EXLCZ)995580000000300707 100 $a20202204d2021 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFoundations of General Relativity$eFrom Einstein to Black Holes 210 $aNijmegen$cRadboud University Press$d2021 215 $a1 electronic resource (394 pages) 311 $a90-831789-2-7 330 $aThis 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. 517 $aFoundations of General Relativity 606 $aRiemannian geometry 606 $aDifferential geometry 606 $aRelativity physics 606 $aHistory 606 $aMathematics 606 $aTopology 610 $aMathematical physics 610 $aPenrose 610 $aGravity 610 $aEinstein 610 $aBlack holes 610 $aMathematical Relativity 615 0$aRiemannian geometry. 615 0$aDifferential geometry. 615 0$aRelativity physics 615 0$aHistory. 615 0$aMathematics. 615 0$aTopology. 700 $aLandsman$b Klaas$4auth$0821832 906 $aBOOK 912 $a9910557840203321 996 $aFoundations of General Relativity$93032292 997 $aUNINA