The formation of black holes in general relativity
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
EMS
2009
|
| Schriftenreihe: | EMS monographs in mathematics
|
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| Online-Zugang: | Inhaltsverzeichnis |
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| 007 | t| | ||
| 008 | 090703s2009 xx |||| 00||| eng d | ||
| 020 | |a 9783037190685 |9 978-3-0371-9068-5 | ||
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| 100 | 1 | |a Christodulu, Dēmētrēs Ch. |d 1951- |e Verfasser |0 (DE-588)1049266897 |4 aut | |
| 245 | 1 | 0 | |a The formation of black holes in general relativity |c Demetrios Christodoulou |
| 264 | 1 | |a Zürich |b EMS |c 2009 | |
| 300 | |a IX, 589 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS monographs in mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Black holes (Astronomy) |x Mathematics | |
| 650 | 4 | |a General relativity (Physics) |x Mathematics | |
| 650 | 4 | |a Gravitational waves |x Mathematics | |
| 650 | 0 | 7 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwarzes Loch |0 (DE-588)4053793-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Schwarzes Loch |0 (DE-588)4053793-6 |D s |
| 689 | 0 | 1 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |a Christodoulou, Demetrios, 1951- |t The formation of black holes in general relativity |n Online-Ausgabe |z 978-3-03719-568-0 |w (DE-604)BV036705952 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017653724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017653724 | |
Datensatz im Suchindex
| DE-BY-UBR_call_number | 803/UH 8300 C556 F7 |
|---|---|
| DE-BY-UBR_katkey | 4503597 |
| DE-BY-UBR_media_number | TEMP12176931 |
| _version_ | 1822671837059874816 |
| adam_text | Contents
Prologue
...................................... 1
1
The Optical Structure Equations
1.1
The basic geometric setup
........................ 29
1.2
The optical structure equations
...................... 33
1.3
The Bianchi equations
.......................... 54
1.4
Canonical coordinate systems
....................... 59
2
The Characteristic Initial Data
2.1
The characteristic initial data
....................... 63
2.2
Construction of the solution in an initial domain
............. 88
3
L°° Estimates for the Connection Coefficients
3.1
Introduction
................................ 91
3.2
L°° estimates for/
............................ 94
3.3
L°° estimates for
χ
............................ 98
3.4
L°° estimates for
η,η_
........................... 102
3.5
L00
estimates for
ω, ω ..........................
107
3.6
The smallness requirement on
б
.....................
Ill
4
L4(5) Estimates for the
1st
Derivatives of the Connection Coefficients
4.1
Introduction
................................ 115
4.2
L4(S) estimates for
Ух
.......................... 128
4.3
L4(S) estimates for
ψχ_
.......................... 131
4.4
L4(S) estimates for
ψη, Τη_........................
135
4.5
L4 (S)
estimates
for
<βω, φω_
........................ 141
4.6
LA(S) estimates for Deo, Deo
....................... 144
5
The Uniformization Theorem
5.1
Introduction. An L2(S) estimate for K- ~K
............... 147
5.2
Sobolev inequalities on S. The isoperimetric constant
.......... 153
5.3
The uniformization theorem
....................... 162
5.4
LP elliptic theory on
5.......................... 170
viu
Contents
6
L4 (S)
Estimates for the
2nd
Derivatives of the Connection Coefficients
6.1
Introduction
................................ 181
6.2
L4(S) estimates for
f
2χ,Κ-
1.................... 182
6.3
L4(S)
estimates
for
ψ 2χ_
......................... 187
6.4
L4(S) estimates for
Ţ
2η, ψ2η
...................... 193
6.5
L4(S)
estimate for
Ţ
2ω .........................
206
6.6
L4(S)
estimate
for
ψ 2ω
......................... 212
7
L2
Estimates for the
3rd
Derivatives of the Connection Coefficients
7.1
Introduction
................................ 215
7.2
L2 estimates for
ψ 2η, ψ 2η_
........................ 216
7.3
L2
elliptic theory for generalized Hodge systems on
S
.......... 221
7.4
L2(S) estimates for
ψ 3χ ,<βΚ......................
233
7.5
L2
estimates for
У Зх
.......................... 238
7.6
L2
estimates for
ψ 3η, ψ 3η_
........................ 242
7.7
L2
estimate for
ψ 3ω
........................... 256
7.8
L2
estimates for
ψ 2ω
and
ψ 3ω
..................... 263
7.9
L2
estimates for
φΌω,
tfDw,
Ό2ω, Ο_2ω
................. 267
8
The Multiplier Fields and the Commutation Fields
8.1
Introduction
................................ 275
8.2
L°° estimates for the deformation tensors of
L, K
and
S
........ 277
8.3
Construction of the rotation vectorfields
О;
............... 281
8.4
I00 estimates for the
О,-
and
у О; ....................
287
8.5
L°° estimates for the deformation tensors of the
O¡
........... 292
9
Estimates for the Derivatives of the
Deformation Tensors of the Commutation Fields
9.1
Estimates for the
1
st derivatives of the deformation
tensors of
L, S
.............................. 299
9.2
Estimates for the
1
st derivatives of the deformation
tensors of the Oi
............................. 301
9.3
Estimates for the
2nd
derivatives of the deformation
tensors of
L, S
.............................. 313
9.4
Estimates for the
2nd
derivatives of the deformation
tensors of the Oi
............................. 316
10
The Sobolev Inequalities on the Cu and the CH
10.1
Introduction
................................ 325
10.2
The Sobolev inequalities on the Cu
.................... 328
10.3
The Sobolev inequalities on the
£.................... 336
Contents ix
11 The S-tangential Derivatives
and the Rotational Lie
Derivatives
11.1
Introduction and preliminaries
...................... 343
11.2
The coercivity inequalities on the standard sphere
............ 349
11.3
The coercivity inequalities on
5„)М
.................... 354
12
Weyl Fields and Currents. The Existence Theorem
12.1
Weyl fields and
Bianchi
equations. Weyl currents
............ 365
12.2
Null decompositions of Weyl fields and currents
............. 370
12.3
The Bel-Robinson tensor. The energy-momentum density
vectorfields
................................ 377
12.4
The divergence theorem in spacetime
................... 378
12.5
The energies and fluxes. The quantity
Т>г
................ 381
12.6
The controlling quantity
Ô2·
Bootstrap assumptions and
the comparison lemma
.......................... 390
12.7
Statement of the existence theorem. Outline of the continuity
argument
................................. 411
13
The Multiplier Error Estimates
13.1
Preliminaries
............................... 423
13.2
The multiplier error estimates
....................... 428
14
The lst-Order Weyl Current Error Estimates
14.1
Introduction
................................ 441
14.2
The error estimates arising from Jl
................... 446
14.3
The error estimates arising from J2
................... 462
14.4
The error estimates arising from
У3
................... 468
15
The Znd-Order Weyl Current Error Estimates
15.1
The
2nd-order
estimates which are of the same form
as the lst-order estimates
......................... 481
15.2
The genuine
ппа-отает
estimates
..................... 493
16
The Energy-Flux Estimates. Completion of the Continuity Argument
16.1
The energy-flux estimates
......................... 517
16.2
Higher-order bounds
........................... 521
16.3
Completion of the continuity argument
.................. 551
16.4
Restatement of the existence theorem
.................. 571
17
Trapped Surface Formation
.......................... 573
Bibliography
.................................... 583
Index
........................................ 587
|
| any_adam_object | 1 |
| author | Christodulu, Dēmētrēs Ch. 1951- |
| author_GND | (DE-588)1049266897 |
| author_facet | Christodulu, Dēmētrēs Ch. 1951- |
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| callnumber-first | Q - Science |
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| classification_rvk | UH 8300 |
| ctrlnum | (OCoLC)317355000 (DE-599)BVBBV035598635 |
| dewey-full | 530.11/ |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.11/ |
| dewey-search | 530.11/ |
| dewey-sort | 3530.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV035598635 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T22:03:23Z |
| institution | BVB |
| isbn | 9783037190685 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017653724 |
| oclc_num | 317355000 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-11 DE-703 DE-188 DE-19 DE-BY-UBM DE-83 DE-29T |
| physical | IX, 589 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | EMS |
| record_format | marc |
| series2 | EMS monographs in mathematics |
| spellingShingle | Christodulu, Dēmētrēs Ch. 1951- The formation of black holes in general relativity Mathematik Black holes (Astronomy) Mathematics General relativity (Physics) Mathematics Gravitational waves Mathematics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Schwarzes Loch (DE-588)4053793-6 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4053793-6 |
| title | The formation of black holes in general relativity |
| title_auth | The formation of black holes in general relativity |
| title_exact_search | The formation of black holes in general relativity |
| title_full | The formation of black holes in general relativity Demetrios Christodoulou |
| title_fullStr | The formation of black holes in general relativity Demetrios Christodoulou |
| title_full_unstemmed | The formation of black holes in general relativity Demetrios Christodoulou |
| title_short | The formation of black holes in general relativity |
| title_sort | the formation of black holes in general relativity |
| topic | Mathematik Black holes (Astronomy) Mathematics General relativity (Physics) Mathematics Gravitational waves Mathematics Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Schwarzes Loch (DE-588)4053793-6 gnd |
| topic_facet | Mathematik Black holes (Astronomy) Mathematics General relativity (Physics) Mathematics Gravitational waves Mathematics Allgemeine Relativitätstheorie Schwarzes Loch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017653724&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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