The formation of black holes in general relativity

Contents......Page 8
Prologue......Page 12
1 The Optical Structure Equations......Page 40
2 The Characteristic Initial Data......Page 74
3 L^\infty Estimates for the Connection Coefficients......Page 102
4 L^4(S) Estimates for the 1st Derivatives of the Connection Coefficients......Page 126
5 The Uniformization Theorem......Page 158
6 L^4(S) Estimates for the 2nd Derivatives of the Connection Coefficients......Page 192
7 L^2 Estimates for the 3rd Derivatives of the Connection Coefficients......Page 226
8 The Multiplier Fields and the Commutation Fields......Page 286
9 Estimates for the Derivatives of the Deformation Tensors of the Commutation Fields......Page 310
10 The Sobolev Inequalities on the C_u and the C_u......Page 336
11 The S-tangential Derivatives and the Rotational Lie Derivatives......Page 354
12 Weyl Fields and Currents. The Existence Theorem......Page 376
13 The Multiplier Error Estimates......Page 434
14 The 1st-Order Weyl Current Error Estimates......Page 452
15 The 2nd-Order Weyl Current Error Estimates......Page 492
16 The Energy-Flux Estimates. Completion of the Continuity Argument......Page 528
17 Trapped Surface Formation......Page 584
Bibliography......Page 594
Index......Page 598