The Cauchy Problem in General Relativity

  • Hans Ringström

    KTH Mathematics, Stockholm, Sweden
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FrontmatterDownload pp. i–v
PrefaceDownload p. vii
ContentsDownload pp. ix–xiii
1IntroductionDownload pp. 1–5
2Outlinepp. 6–18
IPart I Background from the theory of partial differential equationsp. 19
3Functional analysispp. 21–25
4The Fourier transformpp. 26–32
5Sobolev spacespp. 33–44
6Sobolev embeddingpp. 45–56
7Symmetric hyperbolic systemspp. 57–68
8Linear wave equationspp. 69–75
9Local existence, non-linear wave equationspp. 76–91
IIPart II Background in geometry, global hyperbolicity and uniquenessp. 93
10Basic Lorentz geometrypp. 95–110
11Characterizations of global hyperbolicitypp. 111–130
12Uniqueness of solutions to linear wave equationspp. 131–144
IIIPart III General relativityp. 145
13The constraint equationspp. 147–151
14Local existencepp. 152–163
15Cauchy stabilitypp. 164–175
16Existence of a maximal globally hyperbolic developmentpp. 176–183
IVPart IV Pathologies, strong cosmic censorshipp. 185
17Preliminariespp. 187–195
18Constant mean curvaturepp. 196–205
19Initial datapp. 206–212
20Einstein’s vacuum equationspp. 213–224
21Closed universe recollapsepp. 225–231
22Asymptotic behaviourpp. 232–242
23LRS Bianchi class A solutionspp. 243–251
24Existence of extensionspp. 252–259
25Existence of inequivalent extensionspp. 260–264
VPart V Appendicesp. 265
AAppendix App. 267–276
BAppendix Bpp. 277–284
Bibliographypp. 285–289
Indexpp. 291–294

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