Numerical relativity: starting from scratch
"This completely updated edition brings the reader even more handy tips on how to help combat the climate emergency and other environmental problems. New to this edition are: an expanded "What can I do?" section; coverage of Extinction Rebellion, school children marches, the role of p...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York
Cambridge University Press
2021
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This completely updated edition brings the reader even more handy tips on how to help combat the climate emergency and other environmental problems. New to this edition are: an expanded "What can I do?" section; coverage of Extinction Rebellion, school children marches, the role of protest; more for the business community on offsetting, Carbon net zero, and investing; the effects of pandemics and COVID-19; Australian wildfires. Feeding the world, climate change, biodiversity, antibiotics, plastics - the list of concerns seems endless. Given the global nature of the challenges we face, what can any of us DO? Mike Berners-Lee has crunched the numbers and plotted a course of action that is practical and enjoyable. Readers will find the big-picture perspective on the environmental and economic challenges of the day laid out in one place, and traced through to the underlying roots - questions of how we live and think on Planet A"-- |
| Beschreibung: | Im Impressum bezeichnet als: "Updated edition" |
| Beschreibung: | xiv, 220 Seiten Illustrationen, Diagramme |
| ISBN: | 9781108844116 9781108928250 |
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Datensatz im Suchindex
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| adam_text | Contents Preface 1 1.1 1.2 1.3 page ix Newton’s and Einstein’s Gravity A Brief Review of Newton’s Gravity A First Acquaintance with Einstein’s Gravity 1.2.1 The Metric 1.2.2 The Geodesic Equation and the Covariant Derivative 1.2.3 Geodesic Deviation and the Riemann Tensor 1.2.4 Einstein’s Field Equations Two Important Analytical Solutions 1.3.1 Schwarzschild Black Holes 1.3.2 Gravitational Waves Foliations of Spacetime: Constraint and Evolution Equations 2.1 Scalar Fields 2.2 Electrodynamics 2.2.1 Maxwell’s Equations 2.2.2 The Faraday Tensor 2.2.3 “Spacetime Kinematics”: the 3+1 Split of Spacetime 2.2.4 The 3+1 Split of Electrodynamics 2.3 The 3+1 Split of General Relativity 2.4 Comparison and Outlook 1 1 8 9 16 20 23 26 26 33 2 3 3.1 3.2 Solving the Constraint Equations Freely Specifiable versus Constrained Variables Solving the Hamiltonian Constraint 3.2.1 Conformal Decompositions 43 43 46 46 48 54 58 70 82 87 87 89 89
Contents vi 3.2.2 Schwarzschild and Brill-Lindquist Solutions Solving the Momentum Constraints 3.3.1 The Conformal Transverse-Traceless Decomposition 3.3.2 Bowen֊York Solutions Puncture Initial Data for Black Holes Discussion 94 97 101 104 Solving the Evolution Equations Reformulating the Evolution Equations 4.1.1 Maxwell’s Equations 4.1.2 Einstein’s Equations 4.2 Slicing and Gauge Conditions 4.2.1 Geodesic Slicing 4.2.2 Maximal Slicing 4.2.3 Harmonic Slicing 4.2.4 1 + log Slicing and the Gamma-Driver Condition 106 106 107 111 117 117 118 119 120 5 5.1 5.2 5.3 5.4 123 123 128 131 134 3.3 3.4 3.5 4 4.1 Numerical Simulations of Black-Hole Binaries Binary Black Holes and Gravitational Waves Black-Hole Excision and the Moving-Puncture Method Orbital Hang-up, Black-Hole Recoil, andSpin Flips Gravitational Wave Catalogs 91 94 Epilogue 138 Appendix A: A Brief Review of Tensor Properties A.l Expansion into Basis Vectors and One-Forms A.2 Change of Basis A. 3 The Covariant Derivative 140 140 143 146 Appendix B: A Brief Introduction to Some Numerical Techniques B. l Functions and Derivatives B.2 Boundary-Value Problems B.2.1 Linear Problems B.2.2 Nonlinear Problems B.2.3 A Worked Example:Puncture Initial Data B.3 Initial-Value Problems В .3.1 The Method of Lines B.3.2 A Worked Example:Maxwell’s Equations B.4 Convergence Tests 151 151 155 155 158 160 169 169 172 187
Contents vii Appendix C: A Very Brief Introduction to Matter Sources C.l Electromagnetic Fields C. 2 Scalar Fields 190 191 193 Appendix D: A Summary of Important Results D. l Differential Geometry D.2 General Relativity D.3 The 3+1 Decomposition D.4 The Equations of Gauss, Codazzi, Mainardi, and Ricci D.5 The ADM Equations D.6 Conformal Decompositions 195 195 197 197 198 199 199 Appendix E: 200 Answers to SelectedProblems References Index 202 212
|
| adam_txt |
Contents Preface 1 1.1 1.2 1.3 page ix Newton’s and Einstein’s Gravity A Brief Review of Newton’s Gravity A First Acquaintance with Einstein’s Gravity 1.2.1 The Metric 1.2.2 The Geodesic Equation and the Covariant Derivative 1.2.3 Geodesic Deviation and the Riemann Tensor 1.2.4 Einstein’s Field Equations Two Important Analytical Solutions 1.3.1 Schwarzschild Black Holes 1.3.2 Gravitational Waves Foliations of Spacetime: Constraint and Evolution Equations 2.1 Scalar Fields 2.2 Electrodynamics 2.2.1 Maxwell’s Equations 2.2.2 The Faraday Tensor 2.2.3 “Spacetime Kinematics”: the 3+1 Split of Spacetime 2.2.4 The 3+1 Split of Electrodynamics 2.3 The 3+1 Split of General Relativity 2.4 Comparison and Outlook 1 1 8 9 16 20 23 26 26 33 2 3 3.1 3.2 Solving the Constraint Equations Freely Specifiable versus Constrained Variables Solving the Hamiltonian Constraint 3.2.1 Conformal Decompositions 43 43 46 46 48 54 58 70 82 87 87 89 89
Contents vi 3.2.2 Schwarzschild and Brill-Lindquist Solutions Solving the Momentum Constraints 3.3.1 The Conformal Transverse-Traceless Decomposition 3.3.2 Bowen֊York Solutions Puncture Initial Data for Black Holes Discussion 94 97 101 104 Solving the Evolution Equations Reformulating the Evolution Equations 4.1.1 Maxwell’s Equations 4.1.2 Einstein’s Equations 4.2 Slicing and Gauge Conditions 4.2.1 Geodesic Slicing 4.2.2 Maximal Slicing 4.2.3 Harmonic Slicing 4.2.4 1 + log Slicing and the Gamma-Driver Condition 106 106 107 111 117 117 118 119 120 5 5.1 5.2 5.3 5.4 123 123 128 131 134 3.3 3.4 3.5 4 4.1 Numerical Simulations of Black-Hole Binaries Binary Black Holes and Gravitational Waves Black-Hole Excision and the Moving-Puncture Method Orbital Hang-up, Black-Hole Recoil, andSpin Flips Gravitational Wave Catalogs 91 94 Epilogue 138 Appendix A: A Brief Review of Tensor Properties A.l Expansion into Basis Vectors and One-Forms A.2 Change of Basis A. 3 The Covariant Derivative 140 140 143 146 Appendix B: A Brief Introduction to Some Numerical Techniques B. l Functions and Derivatives B.2 Boundary-Value Problems B.2.1 Linear Problems B.2.2 Nonlinear Problems B.2.3 A Worked Example:Puncture Initial Data B.3 Initial-Value Problems В .3.1 The Method of Lines B.3.2 A Worked Example:Maxwell’s Equations B.4 Convergence Tests 151 151 155 155 158 160 169 169 172 187
Contents vii Appendix C: A Very Brief Introduction to Matter Sources C.l Electromagnetic Fields C. 2 Scalar Fields 190 191 193 Appendix D: A Summary of Important Results D. l Differential Geometry D.2 General Relativity D.3 The 3+1 Decomposition D.4 The Equations of Gauss, Codazzi, Mainardi, and Ricci D.5 The ADM Equations D.6 Conformal Decompositions 195 195 197 197 198 199 199 Appendix E: 200 Answers to SelectedProblems References Index 202 212 |
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| spelling | Baumgarte, Thomas W. 1966- Verfasser (DE-588)141868953 aut Numerical relativity starting from scratch Thomas W. Baumgarte, Bowdoin College, Stuart L. Shapiro, University of Illinois at Urbana-Champaign Cambridge ; New York Cambridge University Press 2021 xiv, 220 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Im Impressum bezeichnet als: "Updated edition" "This completely updated edition brings the reader even more handy tips on how to help combat the climate emergency and other environmental problems. New to this edition are: an expanded "What can I do?" section; coverage of Extinction Rebellion, school children marches, the role of protest; more for the business community on offsetting, Carbon net zero, and investing; the effects of pandemics and COVID-19; Australian wildfires. Feeding the world, climate change, biodiversity, antibiotics, plastics - the list of concerns seems endless. Given the global nature of the challenges we face, what can any of us DO? Mike Berners-Lee has crunched the numbers and plotted a course of action that is practical and enjoyable. Readers will find the big-picture perspective on the environmental and economic challenges of the day laid out in one place, and traced through to the underlying roots - questions of how we live and think on Planet A"-- Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Einstein-Feldgleichungen (DE-588)4013941-4 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf General relativity (Physics) Einstein field equations Numerical calculations Allgemeine Relativitätstheorie (DE-588)4112491-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Einstein-Feldgleichungen (DE-588)4013941-4 s Shapiro, Stuart L. 1947- Sonstige (DE-588)136673570 oth Erscheint auch als Online-Ausgabe, EPUB 978-1-108-93344-5 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032537926&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baumgarte, Thomas W. 1966- Numerical relativity starting from scratch Numerisches Verfahren (DE-588)4128130-5 gnd Einstein-Feldgleichungen (DE-588)4013941-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4013941-4 (DE-588)4112491-1 |
| title | Numerical relativity starting from scratch |
| title_auth | Numerical relativity starting from scratch |
| title_exact_search | Numerical relativity starting from scratch |
| title_exact_search_txtP | Numerical relativity starting from scratch |
| title_full | Numerical relativity starting from scratch Thomas W. Baumgarte, Bowdoin College, Stuart L. Shapiro, University of Illinois at Urbana-Champaign |
| title_fullStr | Numerical relativity starting from scratch Thomas W. Baumgarte, Bowdoin College, Stuart L. Shapiro, University of Illinois at Urbana-Champaign |
| title_full_unstemmed | Numerical relativity starting from scratch Thomas W. Baumgarte, Bowdoin College, Stuart L. Shapiro, University of Illinois at Urbana-Champaign |
| title_short | Numerical relativity |
| title_sort | numerical relativity starting from scratch |
| title_sub | starting from scratch |
| topic | Numerisches Verfahren (DE-588)4128130-5 gnd Einstein-Feldgleichungen (DE-588)4013941-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Numerisches Verfahren Einstein-Feldgleichungen Allgemeine Relativitätstheorie |
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