LEADER 02757nam 22003855a 450 001 9910151932503321 005 20091109150325.0 010 $a3-03719-553-3 024 70$a10.4171/053 035 $a(CKB)3710000000953850 035 $a(CH-001817-3)99-091109 035 $a(PPN)178155608 035 $a(EXLCZ)993710000000953850 100 $a20091109j20090608 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aThe Cauchy Problem in General Relativity$b[electronic resource] /$fHans Ringstro?m 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2009 215 $a1 online resource (307 pages) 225 0 $aESI Lectures in Mathematics and Physics (ESI) 330 $aThe general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemai?tre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those wishing to enter the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included. 606 $aDifferential equations$2bicssc 606 $aRelativity and gravitational theory$2msc 615 07$aDifferential equations 615 07$aRelativity and gravitational theory 686 $a83-xx$2msc 700 $aRingstro?m$b Hans$0521400 801 0$bch0018173 906 $aBOOK 912 $a9910151932503321 996 $aThe Cauchy Problem in General Relativity$92565747 997 $aUNINA LEADER 01516nam 2200373 n 450 001 996394683203316 005 20221108045853.0 035 $a(CKB)3810000000009646 035 $a(EEBO)2240859256 035 $a(UnM)99829449 035 $a(UnM)9928069100971 035 $a(EXLCZ)993810000000009646 100 $a19950607d1697 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 10$aLetters of the Cardinal-Duke de Richelieu$b[electronic resource] $egreat minister of state to Lewis XIII. of France. Faithfully translated from the original; by T.B. In two volumes. Vol. I 210 $aLondon $cprinted for A. Roper, R. Clavel, J. Sturton, and A. Bosvile, in Fleet-street$d1697 215 $a[8], 128, 149-305, 304-314; 288 p., [1] leaf of plates, (port.) 300 $aWith an errata at foot of A4v. 300 $aVolume 2 has separate pagination and register; caption title on p. 1 (² A1) reads: Cardinal Richlieu's letters. Vol. II. 300 $aText is contiuous despite pagination. 300 $aReproduction of the original in the British Library. 330 $aeebo-0018 607 $aFrance$xHistory$yLouis XIII, 1610-1643$vEarly works to 1800 700 $aRichelieu$b Armand Jean du Plessis$cduc de,$f1585-1642.$0262964 701 $aT. B$01004222 801 0$bCu-RivES 801 1$bCu-RivES 801 2$bCStRLIN 801 2$bWaOLN 906 $aBOOK 912 $a996394683203316 996 $aLetters of the Cardinal-Duke de Richelieu$92308081 997 $aUNISA