# The Formation of Black Holes in General Relativity

• ### Demetrios Christodoulou

ETH Zürich, Switzerland

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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