Creation of fermions by rotating charged black holes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
SMF
2009 [erschienen] 2010
|
| Series: | Mémoire de la Société Mathématique de France; 117
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | 158 S. |
| ISBN: | 9782856292846 |
Staff View
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| 100 | 1 | |a Häfner, Dietrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Creation of fermions by rotating charged black holes |c Dietrich Häfner |
| 264 | 1 | |a Paris |b SMF |c 2009 [erschienen] 2010 | |
| 300 | |a 158 S. | ||
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Record in the Search Index
| _version_ | 1817704620868239360 |
|---|---|
| adam_text |
CONTENTS
1.
Introduction
. 7
Notations
. 10
Acknowledgments
. 11
2.
Strategy of the proof and
organization of the article
. 13
2.1.
The analytic problem
. 13
2.2.
Strategy of the proof
. 15
2.3.
Organization of the article
. 17
3.
The model of the collapsing star
. 19
3.1.
The Kerr-Newman metric
. 19
3.1.1.
Boyer-Lindquist coordinates
. 19
3.1.2.
Some remarks about geodesies in the Kerr-Newman space-time
. 21
3.2.
The model of the collapsing star
. 26
3.2.1.
Timelike geodesies with L= Q = E
= 0 . 26
3.2.2.
Precise assumptions
. 31
4.
Classical Dirac Fields
. 35
4.1.
Main results
. 35
4.2.
Spin structures
. 36
4.3.
The Dirac equation and the Newman-Penrose formalism
. 37
4.4.
The Dirac equation on block I
. 41
4.4.1.
A new Newman-Penrose tetrad
. 41
4.4.2.
The new expression of the Dirac equation
. 44
4.4.3.
Scattering results
. 48
4.5.
The Dirac equation on Mco\
. 52
5.
Dirac Quantum Fields
. 59
5.1.
Second Quantization of Dirac Fields
. 59
5.2.
Quantization in a globally hyperbolic space-time
. 63
5.3.
The Hawking effect
. 64
6.
Additional scattering results
. 67
6.1.
Spin weighted spherical harmonics
. 67
CONTENTS
6.2.
Velocity estimates
. 68
6.3.
Wave operators
. 70
6.4.
Regularity results
. 72
7.
The characteristic Cauchy problem
. 77
7.1.
Main results
. 77
7.2.
The Cauchy problem with data on a lipschitz space-like hypersurface
. 81
7.3.
Proof of Theorems
7.1
and
7.2 . 85
7.4.
The characteristic Cauchy problem on Mco\
. 87
8.
Reductions
. 91
8.1.
The key theorem
. 91
8.2.
Fixing the angular momentum
. 92
8.3.
The basic problem
. 94
8.4.
The mixed problem for the asymptotic dynamics
. 96
8.5.
The new hamiltonians
. 97
9.
Comparison of the dynamics
. 99
9.1.
Comparison of the characteristic data
. 99
9.2.
Comparison with the asymptotic dynamics
.102
9.3.
Proof of Proposition
9.1 .106
10.
Propagation of singularities
.113
10.1.
The geometric optics approximation and its properties
.115
10.2.
Diagonalization
.117
10.3.
Study of the hamiltonian flow
.123
10.4.
Proof of Proposition
10.1 .126
11.
Proof of the main theorem
.131
11.1.
The energy cut-off
.131
11.2.
The term near the horizon
.135
11.3.
Proof of Theorem
8.2 .138
A. Proof of Proposition
8.2 .139
B. Penrose Compactiflcation of block
J
.147
B.I. Kerr-star and star-Kerr coordinates
.147
B.2. Kruskal-Boyer-Lindquist coordinates
.149
B.3. Penrose compactification of Block
/ .151
Bibliography
.155
MEMOIRES DE LA
SMF
117
This work is devoted to the mathematical study of the Hawking effect for
fermions
in the setting of the collapse of a rotating charged star. We show that an observer
who is located far away from the star and at rest with respect to the Boyer Lindquist
coordinates observes the emergence of a thermal state when his proper time goes to
infinity. We first introduce a model of the collapse of the star. We suppose that the
space-time outside the star is given by the Kerr-Newman metric. The assumptions
on the asymptotic behavior of the surface of the star are inspired by the asymptotic
behavior of certain timelike geodesies in the Kerr-Newman metric. The Dirac equation
is then written using coordinates and a Newman-Penrose tetrad which are adapted
to the collapse. This coordinate system and tetrad are based on the so called simple
null geodesies. The quantization of Dirac fields in a globally hyperbolic space-time is
described. We formulate and prove a theorem about the Hawking effect in this setting.
The proof of the theorem contains a minimal velocity estimate for Dirac fields that
is slightly stronger than the usual ones and an existence and uniqueness result for
solutions of a characteristic Cauchy problem for Dirac fields in the Kerr-Newman
space-time. In an appendix we construct explicitly a Penrose compactification of
block
/
of the Kerr-Newman space-time based on simple null geodesies.
Ce
travail
est conscacré à l'étude mathématique de l'effet
Hawking
pour des fermions
dans le cadre de l'effondrement d'une étoile chargée en rotation. On démontre qu'un
observateur localisé loin de l'étoile et au repos par rapport aux coordonnées de Boyer-
Lindquist observe l'émergence d'un état thermal quand son temps propre tend vers
l'infini. On introduit d'abord un modèle de l'effondrement de l'étoile. On suppose que
l'espace-temps à l'extérieur de l'étoile est donné par la métrique de Kerr-Newman.
Les hypothèses sur le comportement asymptotique de la surface de l'étoile sont
inspirées par le comportement asymptotique de certaines géodésiques de type temps
dans la métrique de Kerr-Newman. L'équation de Dirac est alors écrite en utilisant
des coordonnées et une tétrade de Newman-Penrose adaptées à l'effondrement. Ce
système de coordonnées et cette tétrade sont basés sur des géodésiques qu'on appelle
des géodésiques simples isotropes. La quantification des champs de Dirac dans un
espace-temps globalement hyperbolique est décrite. On formule un théorème sur
l'effet
Hawking
dans ce cadre. La preuve du théorème contient une estimation de
vitesse minimale pour les champs de Dirac légèrement plus forte que les estimations
usuelles ainsi qu'un résultat d'existence et d'unicité pour les solutions d'un problème
caractéristique pour les champs de Dirac dans l'espace-temps de Kerr-Newman. Dans
un appendice, nous construisons explicitement la compactification de Penrose du
bloc
I
de l'espace-temps de Kerr-Newman qui est basée sur les géodésiques simples
isotropes. |
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| id | DE-604.BV036745150 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-06T15:16:51Z |
| institution | BVB |
| isbn | 9782856292846 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020662537 |
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| series2 | Mémoire de la Société Mathématique de France; 117 |
| spelling | Häfner, Dietrich Verfasser aut Creation of fermions by rotating charged black holes Dietrich Häfner Paris SMF 2009 [erschienen] 2010 158 S. txt rdacontent n rdamedia nc rdacarrier Mémoire de la Société Mathématique de France; 117 Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Unruh-Effekt (DE-588)4643880-4 gnd rswk-swf Schwarzes Loch (DE-588)4053793-6 gnd rswk-swf Schwarzes Loch (DE-588)4053793-6 s Quantenfeldtheorie (DE-588)4047984-5 s Unruh-Effekt (DE-588)4643880-4 s DE-604 Société Mathématique de France Mémoire de la Société Mathématique de France 117 (DE-604)BV000000921 117 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020662537&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020662537&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Häfner, Dietrich Creation of fermions by rotating charged black holes Quantenfeldtheorie (DE-588)4047984-5 gnd Unruh-Effekt (DE-588)4643880-4 gnd Schwarzes Loch (DE-588)4053793-6 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4643880-4 (DE-588)4053793-6 |
| title | Creation of fermions by rotating charged black holes |
| title_auth | Creation of fermions by rotating charged black holes |
| title_exact_search | Creation of fermions by rotating charged black holes |
| title_full | Creation of fermions by rotating charged black holes Dietrich Häfner |
| title_fullStr | Creation of fermions by rotating charged black holes Dietrich Häfner |
| title_full_unstemmed | Creation of fermions by rotating charged black holes Dietrich Häfner |
| title_short | Creation of fermions by rotating charged black holes |
| title_sort | creation of fermions by rotating charged black holes |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Unruh-Effekt (DE-588)4643880-4 gnd Schwarzes Loch (DE-588)4053793-6 gnd |
| topic_facet | Quantenfeldtheorie Unruh-Effekt Schwarzes Loch |
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| volume_link | (DE-604)BV000000921 |
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