Introduction to 3+1 numerical relativity:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford University Press
2008
|
| Edition: | 1. publ. |
| Series: | International series of monographs on physics
140 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 444 S. graph. Darst. |
| ISBN: | 9780199205677 |
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| 100 | 1 | |a Alcubierre, Miguel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to 3+1 numerical relativity |c Miguel Alcubierre |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford University Press |c 2008 | |
| 300 | |a XIV, 444 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series of monographs on physics |v 140 | |
| 650 | 7 | |a Espace et temps |2 Rameau | |
| 650 | 7 | |a Relativité (physique) |2 Rameau | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Relativity (Physics) | |
| 650 | 4 | |a Space and time |x Mathematics | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804137907426951168 |
|---|---|
| adam_text | CONTENTS
Brief
review of general relativity
1
1.1
Introduction
1
1.2
Notation and conventions
2
1.3
Special relativity
2
1.4
Manifolds and tensors
7
1.5
The metric tensor
10
1.6
Lie derivatives and Killing fields
14
1.7
Coordinate transformations
17
1.8
Covariant derivatives and geodesies
20
1.9
Curvature
25
1.10
Bianchi
identities and the Einstein tensor
28
1.11
General relativity
28
1.12
Matter and the stress-energy tensor
32
1.13
The Einstein field equations
36
1.14
Weak fields and gravitational waves
39
1.15
The
Schwarzschild
solution and black holes
46
1.16
Black holes with charge and angular momentum
53
1.17
Causal structure, singularities and black holes
57
The
3+1
formalism
64
2.1
Introduction
64
2.2 3+1
split of spacetime
65
2.3
Extrinsic curvature
68
2.4
The Einstein constraints
71
2.5
The ADM evolution equations
73
2.6
Free versus constrained evolution
77
2.7
Hamiltonian formulation
78
2.8
The BSSNOK formulation
81
2.9
Alternative formalisms
87
2.9.1
The characteristic approach
87
2.9.2
The
conformai
approach
90
Initial data
92
3.1
Introduction
92
3.2
York-Lichnerowicz
conformai
decomposition
92
3.2.1
Conformai
transverse decomposition
94
3.2.2
Physical transverse decomposition
97
3.2.3
Weighted transverse decomposition
99
3.3
Conformai
thin-sandwich approach
101
xi
3.4
Multiple black
hole initial
data
105
3.4.1
Time-symmetric data
105
3.4.2
Bowen-York
extrinsic curvature
109
3.4.3
Conformai
factor:
inversions
and punctures 111
3.4.4
Kerr-Schild type data
113
3.5
Binary black holes in quasi-circular orbits
115
3.5.1
Effective potential method
116
3.5.2
The quasi-equilibrium method
117
Gauge conditions
121
4.1
Introduction
121
4.2
Slicing conditions
122
4.2.1
Geodesic slicing and focusing
123
4.2.2
Maximal slicing
123
4.2.3
Maximal slices of
Schwarzschild 127
4.2.4
Hyperbolic slicing conditions
133
4.2.5
Singularity avoidance for hyperbolic slicings
136
4.3
Shift conditions
140
4.3.1
Elliptic shift conditions
141
4.3.2
Evolution type shift conditions
145
4.3.3
Corotating coordinates
151
Hyperbolic reductions of the field equations
155
5.1
Introduction
155
5.2
Well-posedness
156
5.3
The concept of hyperbolicity
158
5.4
Hyperbolicity of the ADM equations
164
5.5
The Bona-Masso and NOR formulations
169
5.6
Hyperbolicity of BSSNOK
175
5.7
The Kidder-Scheel-Teukolsky family
179
5.8
Other hyperbolic formulations
183
5.8.1
Higher derivative formulations
184
5.8.2
The Z4 formulation
185
5.9
Boundary conditions
187
5.9.1
Radiative boundary conditions
188
5.9.2
Maximally dissipative boundary conditions
191
5.9.3
Constraint preserving boundary conditions
194
Evolving black hole spacetimes
198
6.1
Introduction
198
6.2
Isometries and throat adapted coordinates
199
6.3
Static puncture evolution
206
6.4
Singularity avoidance and slice stretching
209
6.5
Black hole excision
214
6.6
Moving punctures
217
xu
6.6.1
How to move the punctures
217
6.6.2
Why does evolving the punctures work?
219
6.7
Apparent horizons
221
6.7.1
Apparent horizons in spherical symmetry
223
6.7.2
Apparent horizons in axial symmetry
224
6.7.3
Apparent horizons in three dimensions
226
6.8
Event horizons
230
6.9
Isolated and dynamical horizons
234
Relativistic hydrodynamics
238
7.1
Introduction
238
7.2
Special relativistic hydrodynamics
239
7.3
General relativistic hydrodynamics
245
7.4 3+1
form of the hydrodynamic equations
249
7.5
Equations of state: dust, ideal gases and polytropes
252
7.6
Hyperbolicity and the speed of sound
257
7.6.1
Newtonian case
257
7.6.2
Relativistic case
260
7.7
Weak solutions and the Riemann problem
264
7.8
Imperfect fluids: viscosity and heat conduction
270
7.8.1
Eckart s irreversible thermodynamics
270
7.8.2
Causal irreversible thermodynamics
273
Gravitational wave extraction
276
8.1
Introduction
276
8.2
Gauge invariant perturbations of
Schwarzschild 277
8.2.1
Multipole expansion
277
8.2.2
Even parity perturbations
280
8.2.3
Odd parity perturbations
283
8.2.4
Gravitational radiation in the TT gauge
284
8.3
The Weyl tensor
288
8.4
The tetrad formalism
291
8.5
The Newman-Penrose formalism
294
8.5.1
Null tetrads
294
8.5.2
Tetrad transformations
297
8.6
The Weyl scalars
298
8.7
The
Petrov
classification
299
8.8
Invariants I and
J
303
8.9
Energy and momentum of gravitational waves
304
8.9.1
The stress-energy tensor for gravitational waves
304
8.9.2
Radiated energy and momentum
307
8.9.3
Multipole decomposition
313
xiii
9
Numerical methods
318
9.1
Introduction
318
9.2
Basic concepts of finite differencing
318
9.3
The one-dimensional wave equation
322
9.3.1
Explicit finite difference approximation
323
9.3.2
Implicit approximation
325
9.4 Von
Newmann stability analysis
326
9.5
Dissipation and dispersion
329
9.6
Boundary conditions
332
9.7
Numerical methods for first order systems
335
9.8
Method of lines
339
9.9
Artificial dissipation and viscosity
343
9.10
High resolution schemes
347
9.10.1
Conservative methods
347
9.10.2
Godunov s method
348
9.10.3
High resolution methods
350
9.11
Convergence testing
353
10
Examples of numerical spacetimes
357
10.1
Introduction
357
10.2
Toy
1+1
relativity
357
10.2.1
Gauge shocks
359
10.2.2
Approximate shock avoidance
362
10.2.3
Numerical examples
364
10.3
Spherical symmetry
369
10.3.1
Reguiarization
370
10.3.2
Hyperbolicity
374
10.3.3
Evolving
Schwarzschild 378
10.3.4
Scalar field collapse
383
10.4
Axial symmetry
391
10.4.1
Evolution equations and reguiarization
391
10.4.2
Brill waves
395
10.4.3
The Cartoon approach
399
A Total mass and momentum in general relativity
402
В
Spacetime Christoffel
symbols in
3+1
language
409
С
BSSNOK with natural
conformai rescaling
410
D
Spin-weighted spherical harmonics
413
References
419
Index
437
XIV
|
| adam_txt |
CONTENTS
Brief
review of general relativity
1
1.1
Introduction
1
1.2
Notation and conventions
2
1.3
Special relativity
2
1.4
Manifolds and tensors
7
1.5
The metric tensor
10
1.6
Lie derivatives and Killing fields
14
1.7
Coordinate transformations
17
1.8
Covariant derivatives and geodesies
20
1.9
Curvature
25
1.10
Bianchi
identities and the Einstein tensor
28
1.11
General relativity
28
1.12
Matter and the stress-energy tensor
32
1.13
The Einstein field equations
36
1.14
Weak fields and gravitational waves
39
1.15
The
Schwarzschild
solution and black holes
46
1.16
Black holes with charge and angular momentum
53
1.17
Causal structure, singularities and black holes
57
The
3+1
formalism
64
2.1
Introduction
64
2.2 3+1
split of spacetime
65
2.3
Extrinsic curvature
68
2.4
The Einstein constraints
71
2.5
The ADM evolution equations
73
2.6
Free versus constrained evolution
77
2.7
Hamiltonian formulation
78
2.8
The BSSNOK formulation
81
2.9
Alternative formalisms
87
2.9.1
The characteristic approach
87
2.9.2
The
conformai
approach
90
Initial data
92
3.1
Introduction
92
3.2
York-Lichnerowicz
conformai
decomposition
92
3.2.1
Conformai
transverse decomposition
94
3.2.2
Physical transverse decomposition
97
3.2.3
Weighted transverse decomposition
99
3.3
Conformai
thin-sandwich approach
101
xi
3.4
Multiple black
hole initial
data
105
3.4.1
Time-symmetric data
105
3.4.2
Bowen-York
extrinsic curvature
109
3.4.3
Conformai
factor:
inversions
and punctures 111
3.4.4
Kerr-Schild type data
113
3.5
Binary black holes in quasi-circular orbits
115
3.5.1
Effective potential method
116
3.5.2
The quasi-equilibrium method
117
Gauge conditions
121
4.1
Introduction
121
4.2
Slicing conditions
122
4.2.1
Geodesic slicing and focusing
123
4.2.2
Maximal slicing
123
4.2.3
Maximal slices of
Schwarzschild 127
4.2.4
Hyperbolic slicing conditions
133
4.2.5
Singularity avoidance for hyperbolic slicings
136
4.3
Shift conditions
140
4.3.1
Elliptic shift conditions
141
4.3.2
Evolution type shift conditions
145
4.3.3
Corotating coordinates
151
Hyperbolic reductions of the field equations
155
5.1
Introduction
155
5.2
Well-posedness
156
5.3
The concept of hyperbolicity
158
5.4
Hyperbolicity of the ADM equations
164
5.5
The Bona-Masso and NOR formulations
169
5.6
Hyperbolicity of BSSNOK
175
5.7
The Kidder-Scheel-Teukolsky family
179
5.8
Other hyperbolic formulations
183
5.8.1
Higher derivative formulations
184
5.8.2
The Z4 formulation
185
5.9
Boundary conditions
187
5.9.1
Radiative boundary conditions
188
5.9.2
Maximally dissipative boundary conditions
191
5.9.3
Constraint preserving boundary conditions
194
Evolving black hole spacetimes
198
6.1
Introduction
198
6.2
Isometries and throat adapted coordinates
199
6.3
Static puncture evolution
206
6.4
Singularity avoidance and slice stretching
209
6.5
Black hole excision
214
6.6
Moving punctures
217
xu
6.6.1
How to move the punctures
217
6.6.2
Why does evolving the punctures work?
219
6.7
Apparent horizons
221
6.7.1
Apparent horizons in spherical symmetry
223
6.7.2
Apparent horizons in axial symmetry
224
6.7.3
Apparent horizons in three dimensions
226
6.8
Event horizons
230
6.9
Isolated and dynamical horizons
234
Relativistic hydrodynamics
238
7.1
Introduction
238
7.2
Special relativistic hydrodynamics
239
7.3
General relativistic hydrodynamics
245
7.4 3+1
form of the hydrodynamic equations
249
7.5
Equations of state: dust, ideal gases and polytropes
252
7.6
Hyperbolicity and the speed of sound
257
7.6.1
Newtonian case
257
7.6.2
Relativistic case
260
7.7
Weak solutions and the Riemann problem
264
7.8
Imperfect fluids: viscosity and heat conduction
270
7.8.1
Eckart's irreversible thermodynamics
270
7.8.2
Causal irreversible thermodynamics
273
Gravitational wave extraction
276
8.1
Introduction
276
8.2
Gauge invariant perturbations of
Schwarzschild 277
8.2.1
Multipole expansion
277
8.2.2
Even parity perturbations
280
8.2.3
Odd parity perturbations
283
8.2.4
Gravitational radiation in the TT gauge
284
8.3
The Weyl tensor
288
8.4
The tetrad formalism
291
8.5
The Newman-Penrose formalism
294
8.5.1
Null tetrads
294
8.5.2
Tetrad transformations
297
8.6
The Weyl scalars
298
8.7
The
Petrov
classification
299
8.8
Invariants I and
J
303
8.9
Energy and momentum of gravitational waves
304
8.9.1
The stress-energy tensor for gravitational waves
304
8.9.2
Radiated energy and momentum
307
8.9.3
Multipole decomposition
313
xiii
9
Numerical methods
318
9.1
Introduction
318
9.2
Basic concepts of finite differencing
318
9.3
The one-dimensional wave equation
322
9.3.1
Explicit finite difference approximation
323
9.3.2
Implicit approximation
325
9.4 Von
Newmann stability analysis
326
9.5
Dissipation and dispersion
329
9.6
Boundary conditions
332
9.7
Numerical methods for first order systems
335
9.8
Method of lines
339
9.9
Artificial dissipation and viscosity
343
9.10
High resolution schemes
347
9.10.1
Conservative methods
347
9.10.2
Godunov's method
348
9.10.3
High resolution methods
350
9.11
Convergence testing
353
10
Examples of numerical spacetimes
357
10.1
Introduction
357
10.2
Toy
1+1
relativity
357
10.2.1
Gauge shocks
359
10.2.2
Approximate shock avoidance
362
10.2.3
Numerical examples
364
10.3
Spherical symmetry
369
10.3.1
Reguiarization
370
10.3.2
Hyperbolicity
374
10.3.3
Evolving
Schwarzschild 378
10.3.4
Scalar field collapse
383
10.4
Axial symmetry
391
10.4.1
Evolution equations and reguiarization
391
10.4.2
Brill waves
395
10.4.3
The "Cartoon" approach
399
A Total mass and momentum in general relativity
402
В
Spacetime Christoffel
symbols in
3+1
language
409
С
BSSNOK with natural
conformai rescaling
410
D
Spin-weighted spherical harmonics
413
References
419
Index
437
XIV |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Alcubierre, Miguel |
| author_facet | Alcubierre, Miguel |
| author_role | aut |
| author_sort | Alcubierre, Miguel |
| author_variant | m a ma |
| building | Verbundindex |
| bvnumber | BV023481195 |
| callnumber-first | Q - Science |
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| callnumber-sort | QC 3173.55 |
| callnumber-subject | QC - Physics |
| classification_rvk | UH 8300 |
| ctrlnum | (OCoLC)191929824 (DE-599)HBZHT015528272 |
| 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 |
| discipline_str_mv | Physik |
| edition | 1. publ. |
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| id | DE-604.BV023481195 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:38:00Z |
| indexdate | 2024-07-09T21:19:45Z |
| institution | BVB |
| isbn | 9780199205677 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016663332 |
| oclc_num | 191929824 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-29T |
| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-29T |
| physical | XIV, 444 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Oxford University Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spelling | Alcubierre, Miguel Verfasser aut Introduction to 3+1 numerical relativity Miguel Alcubierre 1. publ. Oxford [u.a.] Oxford University Press 2008 XIV, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 140 Espace et temps Rameau Relativité (physique) Rameau Mathematik Relativity (Physics) Space and time Mathematics Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Numerische Mathematik (DE-588)4042805-9 s DE-604 Erscheint auch als Online-Ausgabe 9780191709371 International series of monographs on physics 140 (DE-604)BV000106406 140 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alcubierre, Miguel Introduction to 3+1 numerical relativity International series of monographs on physics Espace et temps Rameau Relativité (physique) Rameau Mathematik Relativity (Physics) Space and time Mathematics Numerische Mathematik (DE-588)4042805-9 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4112491-1 |
| title | Introduction to 3+1 numerical relativity |
| title_auth | Introduction to 3+1 numerical relativity |
| title_exact_search | Introduction to 3+1 numerical relativity |
| title_exact_search_txtP | Introduction to 3+1 numerical relativity |
| title_full | Introduction to 3+1 numerical relativity Miguel Alcubierre |
| title_fullStr | Introduction to 3+1 numerical relativity Miguel Alcubierre |
| title_full_unstemmed | Introduction to 3+1 numerical relativity Miguel Alcubierre |
| title_short | Introduction to 3+1 numerical relativity |
| title_sort | introduction to 3 1 numerical relativity |
| topic | Espace et temps Rameau Relativité (physique) Rameau Mathematik Relativity (Physics) Space and time Mathematics Numerische Mathematik (DE-588)4042805-9 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Espace et temps Relativité (physique) Mathematik Relativity (Physics) Space and time Mathematics Numerische Mathematik Allgemeine Relativitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT alcubierremiguel introductionto31numericalrelativity |