Axially symmetric space-times and the characteristic formulation of general relativity:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | III, 195 S. graph. Darst. |
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| 245 | 1 | 0 | |a Axially symmetric space-times and the characteristic formulation of general relativity |c von Thomas Frank Valentin Mädler |
| 264 | 1 | |c 2011 | |
| 300 | |a III, 195 S. |b graph. Darst. | ||
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| 502 | |a München, Techn. Univ., Diss., 2011 | ||
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| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1. GENERAL MOT.IVAT.IOU 1
1.2. COORDINATE SYSTEMS IN GENERAL RELATIVITY 3
1.2.1. COORDINATES: T H E 3+1 APPROACH 3
1.2.2. COORDINATES: T H E LIGHT CONE APPROACH 4
1.2.3. 3+1 APPROACH VS. LIGHT CONE APPROACH 5
1.3. AIMS OF THIS WORK 7
1.4. ORGANIZATION OF THE THESIS 8
1.5. NOTATION AND CONVENTIONS 8
2. SYMMETRIES AND OBSERVERS 11
2.1. INTRODUCTION 11
2.2. THE SPHERICALLY SYMMETRIC SYSTEM 12
2.3. THE AXIALLY SYMMETRIC SYSTEM 12
2.3.1. NEWTONIAN PRELUDE 12
2.3.2. DEFINITION OF AXIAL SYMMETRY IN GENERAL RELATIVITY 14
2.3.3. FURTHER GEOMETRIC IMPLICATIONS OF AXIAL SYMMETRY IN GENERAL REL
ATIVITY 15
2.4. CONSERVED QUANTITIES 21
2.5. CONCLUSION 21
3. THE FIELD EQUATIONS IN BONDI-SACHS COORDINATES 2 3
3.1. MOTIVATION AND OVERVIEW 23
3.1.1. NULL CONES IN MINKOWSKI SPACE 25
3.2. THE BOUDI-SACHS COORDINATES IN AXIAL SYMMETRY 27
3.2.1. THE CONSTRUCTION OF THE COORDINATE SYSTEM 27
3.3. THE EINSTEIN EQUATIONS 35
3.3.1. THE STRUCTURE OF THE EQUATIONS 35
3.4. THE MAIN (. ([NATIONS 37
3.4.1. THE MAIN EQUATIONS IN ABSTRACT INDEX NOTATION 37
3.4.2. T H E MAIN EQUATIONS ILL AXIAL SYMMETRY 41
3.5. GENERAL RELATIVISTIC HYDRODYNAMICS ILL AXIAL SYMMETRY 43
3.5.1. THERMODYNAMICS AND EQUATIONS OF STATE 44
3.5.2. T H E HYDRODYNAMIC EQUATIONS IN AXIAL SYMMETRY AND BONDI-SADIS
COORDINATES 45
3.C. SUMMARY 47
4. VERTEX (I) - FORMALISM 4 9
4.1. INTRODUCTION 49
4.2. THE FERMI NORMAL COORDINATES 4!)
4.2.1. THE METRIC IN FERMI NORMAL COORDINATES 50
4.3. NULL METRICS NEAR A RGULAR TIME-LIKE GEODESIC 53
4.3.1. T H E AFFINE NULL METRIC 53
4.3.2. THE BONDI SACHS METRIC 50
HTTP://D-NB.INFO/1035380129
IMAGE 2
II C O N T E N T S
4.4. SUMMARY AND DISCUSSION 58
5. VERTEX (II) - SOLUTIONS 6 1
5.1. INTRODUCTION (IL
5.2. GENERAL SETUP FIL
5.3. VACUUM SPACE-TIME 02
5.3.1. STATIONARY AXISYMMETRIC VACUUM SPACE-TIME 03
5.3.2. TIME-DEPENDENT. AXISYMMETRIC VACUUM SPACE-TIME 00
5.4. STATIONARY AXISYMMETRIC PERFECT FLUID SPACE-TIME: GENERAL SET-UP .
. . . 70 5.4.1. A GENERAL AXIALLY SYMMETRIC. STATIONARY FLUID NEAR THE
VERTEX . . 71 5.4.2. THE PURELY ROTATING, AXIALLY SYMMETRIC FLUID
SOLUTION 72
5.4.3. THE NON-ROTATING, AXIALLY SYMMETRIC FLUID SOLUTION 77
5.5. COMPARISON WITH THE LITERATURE 7!)
5.0. SUMMARY AND DISCUSSION 80
6. ASYMPTOPIA 8 3
(I.L. ASYMPTOTIC BEHAVIOUR, GRAVITATIONAL WAVES & FRAMES 83
0.1.1. BONDI & SACHS FORMALISM 83
0.1.2. NEWMAN PENROSE FORMALISM 85
0.1.3. PEELING VS. OUTGOING RADIATION CONDITION 80
0.1.4. COORDINATE FRAMES IN THE ASYMPTOTIC REGIME 87
0.2. MAPPING NULL INFINITY TO FINITE VALUES 88
0.3. A REGULAR, FIRST-ORDER REPRESENTATION OF THE MAIN EQUATIONS 8!)
0.3.1. COMPARISON WITH THE LITERATURE !)4
0.4. FIRST-ORDER. REGULAR EQUATIONS IN AXIAL SYMMETRY !MI
0.5. SUMMARY !)8
7. INITIAL MODELS (I) - LINEARIZED WAVES IN VACUO 101
7.1. INTRODUCTION 101
7.2. THE SCALAR WAVE EQUATION 102
7.2.1. FIRST SOLUTION PROCEDURE 103
7.2.2. SECOND SOLUTION PROCEDURE 105
7.2.3. DISCUSSION OF THE TWO SOLUTION APPROACHES 100
7.2.4. DISCUSSION OF THE SOLUTION OF THE SCALAR WAVE EQUATION 107
7.3. THE QUASI-SPHERICAL APPROXIMATION OF THE METRIC 108
7.3.1. FIELD EQUATIONS IN THE -EXPANSION I L L
7.3.2. THE NULL TETRAD AND WCYL SCALARS 113
7.4. LINEARIZED WAVES IN THE VACUUM 114
7.4.1. BACKGROUND MODEL 114
7.4.2. LINEAR PERTURBATIONS 114
7.5. CONCLUSION AND COMPARISON WITH THE LITERATURE 120
8. INITIAL MODELS (II) - SLOWLY ROTATING STARS 123
8.1. PRELUDE 123
8.2. SLOWLY ROTATING NEUTRON STARS IN EQUILIBRIUM 124
8.2.1. QUASI-SPHERICAL APPROXIMATION NEAR THE VERTEX OF TILE NULL CONE .
125 8.2.2. ASSUMPTIONS OU THE INITIAL MODELS 12!)
8.3. TOV EQUATIONS IN BONDI-SACHS COORDINATES 130
8.4. FIRST-ORDER ROTATIONAL PERTURBATIONS 133
8.4.1. MATTER PERTURBATIONS 133
8.4.2. THE PERTURBATIONS OF GROUP G1 134
8.4.3. THE PERTURBATIONS OF GROUP G2 137
IMAGE 3
C O N T E N T S III
8.5. INTERPRETATION OF THE INTEGRATION CONSTANTS 13!)
8.0. THE WINIEOUR ANGULAR MOMENTUM A T J + 144
8.7. CONCLUSIONS 14(I
9. SUMMARY, CONCLUSIONS AND OUTLOOK 149
A. GEOMETRIC AND STELLAR GEOMETRIC UNITS 153
B. ASSOCIATED LEGENDRE POLYNOMIALS 155
C. ASYMPTOTICS: BONDI MASS AND MASS LOSS 157
D. PROOF O F SOME LEMMATA IN THE TEXT 161
D.L. PROOF OF THE LEMMA ON THE STRUCTURE OF THE FIELD EQUATIONS 101
D.2. PROOF OF THE LEINUIA FOR THE COMPACTIFIED EINSTEIN EQUATIONS I (I2
E. NUMERICAL INTEGRATION OF THE EQUILIBRIUM MODELS 165
BIBLIOGRAPHY 177
MAPLE AND GRTENSOR SCRIPTS 178
ACKNOWLEDGMENTS 197
|
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| discipline | Physik |
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| language | English |
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| spelling | Mädler, Thomas Frank Valentin Verfasser aut Axially symmetric space-times and the characteristic formulation of general relativity von Thomas Frank Valentin Mädler 2011 III, 195 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2011 Zylindrische Anordnung (DE-588)4387896-9 gnd rswk-swf Gravitationswelle (DE-588)4158119-2 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Allgemeine Relativitätstheorie (DE-588)4112491-1 s Zylindrische Anordnung (DE-588)4387896-9 s Gravitationswelle (DE-588)4158119-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025874410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mädler, Thomas Frank Valentin Axially symmetric space-times and the characteristic formulation of general relativity Zylindrische Anordnung (DE-588)4387896-9 gnd Gravitationswelle (DE-588)4158119-2 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4387896-9 (DE-588)4158119-2 (DE-588)4112491-1 (DE-588)4113937-9 |
| title | Axially symmetric space-times and the characteristic formulation of general relativity |
| title_auth | Axially symmetric space-times and the characteristic formulation of general relativity |
| title_exact_search | Axially symmetric space-times and the characteristic formulation of general relativity |
| title_full | Axially symmetric space-times and the characteristic formulation of general relativity von Thomas Frank Valentin Mädler |
| title_fullStr | Axially symmetric space-times and the characteristic formulation of general relativity von Thomas Frank Valentin Mädler |
| title_full_unstemmed | Axially symmetric space-times and the characteristic formulation of general relativity von Thomas Frank Valentin Mädler |
| title_short | Axially symmetric space-times and the characteristic formulation of general relativity |
| title_sort | axially symmetric space times and the characteristic formulation of general relativity |
| topic | Zylindrische Anordnung (DE-588)4387896-9 gnd Gravitationswelle (DE-588)4158119-2 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Zylindrische Anordnung Gravitationswelle Allgemeine Relativitätstheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025874410&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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