LEADER 02570nam 22003855a 450 001 9910151935703321 005 20091109150325.0 010 $a3-03719-505-3 024 70$a10.4171/005 035 $a(CKB)3710000000953818 035 $a(CH-001817-3)19-091109 035 $a(PPN)178155314 035 $a(EXLCZ)993710000000953818 100 $a20091109j20080205 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Problems of General Relativity I$b[electronic resource] /$fDemetrios Christodoulou 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2008 215 $a1 online resource (157 pages) 225 0 $aZurich Lectures in Advanced Mathematics (ZLAM) 330 $aGeneral Relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method is the study and systematic use of foliations by characteristic (null) hypersurfaces, and is in the spirit of the approach of Roger Penrose in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction into the methods and applications of general relativity. 606 $aGeneral relativity$2bicssc 606 $aRelativity and gravitational theory$2msc 615 07$aGeneral relativity 615 07$aRelativity and gravitational theory 686 $a83-xx$2msc 700 $aChristodoulou$b Demetrios$0320209 801 0$bch0018173 906 $aBOOK 912 $a9910151935703321 996 $aMathematical Problems of General Relativity I$92567868 997 $aUNINA