02757nam 22003855a 450 991015193250332120091109150325.03-03719-553-310.4171/053(CKB)3710000000953850(CH-001817-3)99-091109(PPN)178155608(EXLCZ)99371000000095385020091109j20090608 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierThe Cauchy Problem in General Relativity[electronic resource] /Hans RingströmZuerich, Switzerland European Mathematical Society Publishing House20091 online resource (307 pages)ESI Lectures in Mathematics and Physics (ESI)The 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-Lemaître-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.Differential equationsbicsscRelativity and gravitational theorymscDifferential equationsRelativity and gravitational theory83-xxmscRingström Hans521400ch0018173BOOK9910151932503321The Cauchy Problem in General Relativity2565747UNINA00889nam0-2200253 --450 991086910000332120240710162940.020240710d1947----kmuy0itay5050 bafreFRaf 001yyComptes rendus de la Conférence de Pédologie Méditerranéenne[Alger - Montpellier, 1er - 20 mai 1947]Association Française pour l'étude du sol[S. l.][s. n.]1947VI, 510 p., [7] c. di tav. di cui 2 ripiegateill.24 cmPedologia631.4423itaAssociation Française pour l'étude du sol1743393ITUNINAREICATUNIMARCBK9910869100003321A MIC 27339683/2024FAGBCFAGBCComptes rendus de la Conférence de Pédologie Méditerranéenne4170814UNINA