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