The Formation of Black Holes in General Relativity

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	FrontmatterDownload pp. i–v
	ContentsDownload pp. vii–ix
	PrologueDownload pp. 1–28
1	The Optical Structure Equationspp. 29–62
2	The Characteristic Initial Datapp. 63–89
3	$L^{\infty}$ Estimates for the Connection Coefficientspp. 91–113
4	$L^{4} (S)$ Estimates for the 1st Derivatives of the Connection Coefficientspp. 115–146
5	The Uniformization Theorempp. 147–179
6	$L^{4} (S)$ Estimates for the 2nd Derivatives of the Connection Coefficientspp. 181–214
7	$L^{2}$ Estimates for the 3rd Derivatives of the Connection Coefficientspp. 215–274
8	The Multiplier Fields and the Commutation Fieldspp. 275–297
9	Estimates for the Derivatives of the Deformation Tensors of the Commutation Fieldspp. 299–324
10	The Sobolev Inequalities on the $C_{u}$ and the $\underline{C}_{\underline{u}}$ pp. 325–342
11	The $S$ -tangential Derivatives and the Rotational Lie Derivativespp. 343–363
12	Weyl Fields and Currents. The Existence Theorempp. 365–421
13	The Multiplier Error Estimatespp. 423–440
14	The 1st-Order Weyl Current Error Estimatespp. 441–480
15	The 2nd-Order Weyl Current Error Estimatespp. 481–516
16	The Energy-Flux Estimates. Completion of the Continuity Argumentpp. 517–571
17	Trapped Surface Formationpp. 573–581
	Bibliographypp. 583–586
	Indexpp. 587–589