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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