The Cauchy Problem in General Relativity

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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