Numerical relativity: solving Einstein's equations on the computer
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVIII, 698 S. Ill., graph. Darst. |
| ISBN: | 9780521514071 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical relativity |b solving Einstein's equations on the computer |c Thomas W. Baumgarte and Stuart L. Shapiro |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XVIII, 698 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804143126479110147 |
|---|---|
| adam_text | Contents
Preface
page
xi
Suggestions for using this book
xvii
1
General relativity preliminaries
1
1.1
Einstein s equations in 4-dimensional spacetime
1
1.2
Black holes
9
1.3
Oppenheimer-Volkoff spherical equilibrium stars
15
1.4
Oppenheimer-Snyder spherical dust collapse
18
2
The
3+1
decompostion of Einstein s equations
23
2.1
Notation and conventions
26
2.2
Maxwell s equations in Minkowski spacetime
27
2.3
Foliations of spacetime
29
2.4
The extrinsic curvature
33
2.5
The equations of Gauss,
Codazzi
and
Ricci
36
2.6
The constraint and evolution equations
39
2.7
Choosing basis vectors: the ADM equations
43
3
Constructing initial data
54
3.1
Conformai
transformations
56
3.1.1
Conformai
transformation of the spatial metric
56
3.1.2
Elementary black hole solutions
57
3.1.3
Conformai
transformation of the extrinsic
curvature
64
3.2
Conformai transverse-traceless
decomposition
67
3.3
Conformai
thin-sandwich decomposition
75
3.4
A step further: the waveless approximation
81
3.5
Mass, momentum and angular momentum
83
4
Choosing coordinates: the lapse and shift
98
4.1
Geodesic slicing
100
4.2
Maximal slicing and singularity avoidance
103
4.3
Harmonic coordinates and variations 111
vi
Contents
4.4
Quasi-isotropic and radial gauge
114
4.5
Minimal distortion and variations
117
5
Matter sources
123
5.1
Vacuum
124
5.2
Hydrodynamics
124
5.2.1
Perfect gases
124
5.2.2
Imperfect gases
139
5.2.3
Radiation hydrodynamics
141
5.2.4
Magnetohydrodynamics
148
5.3
Collisionless matter
163
5.4
Scalar fields
175
6
Numerical methods
183
6.1
Classification of partial differential equations
183
6.2
Finite difference methods
188
6.2.1
Representation of functions and derivatives
188
6.2.2
Elliptic equations
191
6.2.3
Hyperbolic equations
200
6.2.4
Parabolic equations
209
6.2.5
Mesh refinement
211
6.3
Spectral methods
213
6.3.1
Representation of functions and derivatives
213
6.3.2
A simple example
214
6.3.3
Pseudo-spectral methods with Chebychev polynomials
217
6.3.4
Elliptic equations
219
6.3.5
Initial value problems
223
6.3.6
Comparison with finite-difference methods
224
6.4
Code validation and calibration
225
7
Locating black hole horizons
229
7.1
Concepts
229
7.2
Event horizons
232
7.3
Apparent horizons
235
7.3.1
Spherical symmetry
240
7.3.2
Axisymmetry
241
7.3.3
General case: no symmetry assumptions
246
7.4
Isolated and dynamical horizons
249
8
Spherically symmetric spacetimes
253
8.1
Black holes
256
8.2
Collisionless clusters: stability and collapse
266
8.2.1
Particle method
267
8.2.2
Phase space method
289
Contents
vii
8.3
Fluid stars: collapse
291
8.3.1
Misner-Sharp formalism
294
8.3.2
The Hernandez-Misner equations
297
8.4
Scalar field collapse: critical phenomena
303
9
Gravitational waves
311
9.1
Linearized waves
311
9.1.1
Perturbation theory and the weak-field,
slow-velocity regime
312
9.1.2
Vacuum solutions
319
9.2
Sources
323
9.2.1
The high frequency band
324
9.2.2
The low frequency band
328
9.2.3
The very low and ultra low frequency bands
330
9.3
Detectors and templates
331
9.3.1
Ground-based gravitational wave
interferometers
332
9.3.2
Space-based detectors
334
9.4
Extracting gravitational waveforms
337
9.4.1
The gauge-invariant Moncrief formalism
338
9.4.2
The Newman-Penrose formalism
346
10
Collapse of collisionless clusters in axisymmetry
352
10.1
Collapse of prolate spheroids to spindle singularities
352
10.2
Head-on collision of two black holes
359
10.3
Disk collapse
364
10.4
Collapse of rotating toroidal clusters
369
11
Recasting the evolution equations
375
11.1
Notions of
hyperbolicky
376
11.2
Recasting Maxwell s equations
378
11.2.1
Generalized Coulomb gauge
379
11.2.2
First-order hyperbolic formulations
380
11.2.3
Auxiliary variables
381
11.3
Generalized harmonic coordinates
381
11.4
First-order symmetric hyperbolic formulations
384
11.5
The BSSN formulation
386
12
Binary black hole initial data
394
12.
1 Binary
inspirai:
overview
395
12.2
The
conformai
transverse-traceless approach: Bowen-York
403
12.2.1
Solving the momentum constraint
403
12.2.2
Solving the Hamiltonian constraint
405
12.2.3
Identifying circular orbits
407
viii Contents
12.3
The conformai
thin-sandwich approach
410
12.3.1
The notion of quasiequilibium
410
12.3.2
Quasiequilibrium black hole boundary conditions
413
12.3.3
Identifying circular orbits
419
12.4
Quasiequilibrium sequences
421
13
Binary black hole evolution
429
13.1
Handling the black hole singularity
430
13.1.1
Singularity avoiding coordinates
430
13.1.2
Black hole excision
431
13.1.3
The moving puncture method
43 2
13.2
Binary black hole
inspirai
and coalescence
436
13.2.1
Equal-mass binaries
437
13.2.2
Asymmetric binaries, spin and black hole recoil
445
14
Rotating stars
459
14.1
Initial data: equilibrium models
460
14.1.1
Field equations
460
14.1.2
Fluid stars
461
14.1.3
Collisionless clusters
471
14.2
Evolution: instabilities and collapse
473
14.2.1 Quasiradial
stability and collapse
473
14.2.2
Bar-mode instability
478
14.2.3
Black hole excision and stellar collapse
481
14.2.4
Viscous evolution
491
14.2.5
MHD
evolution
495
15
Binary neutron star initial data
506
15.1
Stationary fluid solutions
506
15.1.1
Newtonian equations of stationary equilibrium
508
15.1.2
Relativistic equations of stationary equilibrium
512
15.2
Corotational binaries
514
15.3
Irrotational binaries
523
15.4
Quasiadiabatic
inspirai
sequences
530
16
Binary neutron star evolution
533
16.1
Peliminary studies
534
16.2
The
conformai
flatness approximation
535
16.3
Fully relativistic simulations
545
17
Binary black hole-neutron stars: initial data and evolution
562
17.1
Initial data
565
17.1.1
The
conformai
thin-sandwich approach
565
17.1.2
The
conformai transverse-traceless
approach
5 72
Contents ix
17.2
Dynamical
simulations
574
17.2.1
The conformai
flatness
approximation
574
17.2.2
Fully relativistic
simulations
578
18
Epilogue
596
A Lie
derivatives, Killing vectors, and tensor densities
598
A.I The Lie derivative
598
A.2 Killing vectors
602
A.3 Tensor densities
603
В
Solving the vector Laplacian
607
С
The surface element on the apparent horizon
609
0
Scalar, vector and tensor spherical harmonics
612
E
Post-Newtonian results
616
F
Collisionless matter evolution in axisymmetry: basic equations
629
G
Rotating equilibria: gravitational field equations
634
H
Moving puncture
représentions
of Schwarzschild: analytical results
637
I Binary black hole puncture simulations as test problems
642
References
ЬАІ
Index
684
Aimed at students and researchers entering the
field, this pedagogical introduction to numerical
relativity will also interest scientists seeking a
broad survey of its challenges and achievements.
Assuming only a basic knowledge of classical
general relativity, this textbook develops the
mathematical formalism from first principles, then
highlights some of the pioneering simulations
involving black holes and neutron stars, gravita¬
tional collapse and gravitational waves.
Applications include calculations of coalescing
binary black holes and binary neutron stars,
rotating stars, colliding star clusters, gravita¬
tional and magnetorotational collapse, critical
phenomena, the generation of gravitational
waves, and many more.
• 300
exercises help readers master new material
as it is presented
•
Numerous illustrations, many in color, assist in
visualizing new geometric concepts and high¬
lighting the results of computer simulations
•
Summary boxes encapsulate some of the most
important results for quick reference
•
Applications cover topics of current physical and
astrophysical significance
...
an excellent introduction
. ..
covering
both mathematical aspects and numerical
techniques.
...
The authors are world leaders
in numerical relativity
...
This book will soon
become the standard advanced text for
younger researchers entering the field and
will also serve as the authoritative reference
for senior researchers.
..
Abhay Ashtekhar, Director, Institute for
Gravitation and the Cosmos, The
Pennsylvania State University
Numerical relativity has come of age
...
Two
leading experts give a lucid as well as richly
detailed account building a bridge from
the basics to current research
-
highly
recommended.
Bernd Brügmann, Friedrich-Schiller-
Universität
...
what a book this is!
...
a genuine
learning manual
...
exceedingly well written
...
covers virtually all aspects of numerical
relativity
...
replete with beautiful and
helpful diagrams
...
a useful reference to
the researcher and a source of enlightenment
to many a student.
...
Eric Poisson,
University of Guelph
Baumgarte
and Shapiro are established
leaders in this subject. Their book is a timely
contribution to the literature, and the ideal
primer for researchers newly attracted to the
burgeoning field of computational relativity.
Martin
Rees,
Astronomer Royal and Master
of Trinity College, Cambridge
Cover illustration: a neutron star
inspirais
toward a black hole, gets
tidally disrupted, and merges with the hole. Such a binary merger
is a promising source of gravitational waves. Tracking this
scenario requires a large-scale simulation utilizing the tools of
numerical relativity.
CAMBRIDGE
UNIVERSITY PRESS
www.cambridge.org
ISBN
978-0-521-51407-1
78052Г5Н071
|
| any_adam_object | 1 |
| author | Baumgarte, Thomas W. 1966- Shapiro, Stuart L. 1947- |
| author_GND | (DE-588)141868953 (DE-588)136673570 |
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| author_sort | Baumgarte, Thomas W. 1966- |
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| building | Verbundindex |
| bvnumber | BV036552153 |
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| discipline | Physik |
| edition | 1. publ. |
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| id | DE-604.BV036552153 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:42:41Z |
| institution | BVB |
| isbn | 9780521514071 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020473675 |
| oclc_num | 699562721 |
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| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 DE-11 DE-355 DE-BY-UBR DE-20 |
| physical | XVIII, 698 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Baumgarte, Thomas W. 1966- Verfasser (DE-588)141868953 aut Numerical relativity solving Einstein's equations on the computer Thomas W. Baumgarte and Stuart L. Shapiro 1. publ. Cambridge Cambridge Univ. Press 2010 XVIII, 698 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Einstein-Feldgleichungen (DE-588)4013941-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Einstein-Feldgleichungen (DE-588)4013941-4 s 1\p DE-604 Shapiro, Stuart L. 1947- Verfasser (DE-588)136673570 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020473675&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=020473675&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Baumgarte, Thomas W. 1966- Shapiro, Stuart L. 1947- Numerical relativity solving Einstein's equations on the computer Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Einstein-Feldgleichungen (DE-588)4013941-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4112491-1 (DE-588)4013941-4 (DE-588)4128130-5 |
| title | Numerical relativity solving Einstein's equations on the computer |
| title_auth | Numerical relativity solving Einstein's equations on the computer |
| title_exact_search | Numerical relativity solving Einstein's equations on the computer |
| title_full | Numerical relativity solving Einstein's equations on the computer Thomas W. Baumgarte and Stuart L. Shapiro |
| title_fullStr | Numerical relativity solving Einstein's equations on the computer Thomas W. Baumgarte and Stuart L. Shapiro |
| title_full_unstemmed | Numerical relativity solving Einstein's equations on the computer Thomas W. Baumgarte and Stuart L. Shapiro |
| title_short | Numerical relativity |
| title_sort | numerical relativity solving einstein s equations on the computer |
| title_sub | solving Einstein's equations on the computer |
| topic | Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Einstein-Feldgleichungen (DE-588)4013941-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Allgemeine Relativitätstheorie Einstein-Feldgleichungen Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020473675&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020473675&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT baumgartethomasw numericalrelativitysolvingeinsteinsequationsonthecomputer AT shapirostuartl numericalrelativitysolvingeinsteinsequationsonthecomputer |