LEADER 02722nam 22004335a 450 001 9910151933603321 005 20091109150325.0 010 $a3-03719-568-1 024 70$a10.4171/068 035 $a(CKB)3710000000953839 035 $a(CH-001817-3)93-091109 035 $a(PPN)178155578 035 $a(EXLCZ)993710000000953839 100 $a20091109j20090110 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aThe Formation of Black Holes in General Relativity$b[electronic resource] /$fDemetrios Christodoulou 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2009 215 $a1 online resource (599 pages) 225 0 $aEMS Monographs in Mathematics (EMM) ;$x2523-5192 330 $aIn 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity. A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves. The theorems proved in the present monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler-Lagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable. This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations. 606 $aGeneral relativity$2bicssc 606 $aRelativity and gravitational theory$2msc 606 $aPartial differential equations$2msc 606 $aGlobal analysis, analysis on manifolds$2msc 615 07$aGeneral relativity 615 07$aRelativity and gravitational theory 615 07$aPartial differential equations 615 07$aGlobal analysis, analysis on manifolds 686 $a83-xx$a35-xx$a58-xx$2msc 700 $aChristodoulou$b Demetrios$0320209 801 0$bch0018173 906 $aBOOK 912 $a9910151933603321 996 $aThe Formation of Black Holes in General Relativity$92565447 997 $aUNINA