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Numerical Relativity: Starting from Scratch [Kõva köide]

4.25/5 (7 hinnangut Goodreads-ist)
(Bowdoin College, Maine), (University of Illinois, Urbana-Champaign)
  • Formaat: Hardback, 234 pages, kõrgus x laius x paksus: 235x155x13 mm, kaal: 520 g, Worked examples or Exercises
  • Ilmumisaeg: 08-Apr-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108844111
  • ISBN-13: 9781108844116
Teised raamatud teemal:
Numerical Relativity: Starting from ScratchSuurem pilt
  • Formaat: Hardback, 234 pages, kõrgus x laius x paksus: 235x155x13 mm, kaal: 520 g, Worked examples or Exercises
  • Ilmumisaeg: 08-Apr-2021
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108844111
  • ISBN-13: 9781108844116
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108844116.html
Märksõnad:
Numerical relativity has emerged as the key tool to model gravitational waves that are emitted when two black holes collide. This book provides a pedagogical, accessible and concise introduction to the subject for non-experts, acquainting them with the key concepts underlying publicly available numerical relativity codes.

Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

Arvustused

'Computational general relativity has now become a central tool for the exploration of the astrophysical universe, and gravitational-wave astronomy would not be possible without it. A burgeoning or seasoned astrophysicist who wishes to be up to date must therefore acquire an awareness of the field's methods and main achievements. But where to begin? With this book! Baumgarte and Shapiro are leading experts (indeed, founding experts) of this field, and with their trademark lucid and engaging prose, they take us gently by the hand on a comprehensive guided tour. Mysterious notions (lapse, shift, extrinsic curvature, constraint equations) are introduced seamlessly, and the book features a gallery of the field's most important results to date. A superb achievement for the great benefit of the scientific community.' Eric Poisson, University of Guelph; author of A Relativist's Toolkit 'Numerical relativity well deserves its reputation as a subject of great beauty yet prodigious conceptual difficulty and daunting technical complexity. This outstanding text, by two leading practitioners of the field, is a wonderful Rosetta Stone for those seeking an efficient path toward a working knowledge of the subject. For me it will serve as an essential reference. I'm sorry only that it was not available sooner.' Robert Eisenstein, Massachusetts Institute of Technology 'This is an excellent book explaining the general relativistic two-body problem and its numerical treatment in a highly pedagogical manner to a broad scientific audience. Besides the main topic, readers will also gain some unexpected insight and new viewpoints on numerous wider aspects of Einstein's theory.' Ulrich Sperhake, University of Cambridge 'Black holes and gravitational waves are, thanks to new observations, fast-advancing frontiers of astronomy that attract wide interest. Their implications are best addressed by powerful computers, so this text, by two acknowledged world experts, is especially welcome and timely.' Martin Rees, Astronomer Royal; author of Gravity's Fatal Attraction

Muu info

A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.
Preface ix
1 Newton's and Einstein's Gravity
1(42)
1.1 A Brief Review of Newton's Gravity
1(7)
1.2 A First Acquaintance with Einstein's Gravity
8(18)
1.2.1 The Metric
9(7)
1.2.2 The Geodesic Equation and the Covariant Derivative
16(4)
1.2.3 Geodesic Deviation and the Riemann Tensor
20(3)
1.2.4 Einstein's Field Equations
23(3)
1.3 Two Important Analytical Solutions
26(17)
1.3.1 Schwarzschild Black Holes
26(7)
1.3.2 Gravitational Waves
33(10)
2 Foliations of Spacetime: Constraint and Evolution Equations
43(44)
2.1 Scalar Fields
43(3)
2.2 Electrodynamics
46(24)
2.2.1 Maxwell's Equations
46(2)
2.2.2 The Faraday Tensor
48(6)
2.2.3 "Spacetime Kinematics": the 3+1 Split of Spacetime
54(4)
2.2.4 The 3+1 Split of Electrodynamics
58(12)
2.3 The 3+1 Split of General Relativity
70(12)
2.4 Comparison and Outlook
82(5)
3 Solving the Constraint Equations
87(19)
3.1 Freely Specifiable versus Constrained Variables
87(2)
3.2 Solving the Hamiltonian Constraint
89(5)
3.2.1 Conformal Decompositions
89(2)
3.2.2 Schwarzschild and Brill--Lindquist Solutions
91(3)
3.3 Solving the Momentum Constraints
94(7)
3.3.1 The Conformal Transverse--Traceless Decomposition
94(3)
3.3.2 Bowen--York Solutions
97(4)
3.4 Puncture Initial Data for Black Holes
101(3)
3.5 Discussion
104(2)
4 Solving the Evolution Equations
106(17)
4.1 Reformulating the Evolution Equations
106(11)
4.1.1 Maxwell's Equations
107(4)
4.1.2 Einstein's Equations
111(6)
4.2 Slicing and Gauge Conditions
117(6)
4.2.1 Geodesic Slicing
117(1)
4.2.2 Maximal Slicing
118(1)
4.2.3 Harmonic Slicing
119(1)
4.2.4 1 + log Slicing and the Gamma-Driver Condition
120(3)
5 Numerical Simulations of Black-Hole Binaries
123(15)
5.1 Binary Black Holes and Gravitational Waves
123(5)
5.2 Black-Hole Excision and the Moving-Puncture Method
128(3)
5.3 Orbital Hang-up, Black-Hole Recoil, and Spin Flips
131(3)
5.4 Gravitational Wave Catalogs
134(4)
Epilogue
138(2)
Appendix A A Brief Review of Tensor Properties
140(11)
A.1 Expansion into Basis Vectors and One-Forms
140(3)
A.2 Change of Basis
143(3)
A.3 The Covariant Derivative
146(5)
Appendix B A Brief Introduction to Some Numerical Techniques
151(39)
B.1 Functions and Derivatives
151(4)
B.2 Boundary-Value Problems
155(14)
B.2.1 Linear Problems
155(3)
B.2.2 Nonlinear Problems
158(2)
B.2.3 A Worked Example: Puncture Initial Data
160(9)
B.3 Initial-Value Problems
169(18)
B.3.1 The Method of Lines
169(3)
B.3.2 A Worked Example: Maxwell's Equations
172(15)
B.4 Convergence Tests
187(3)
Appendix C A Very Brief Introduction to Matter Sources
190(5)
C.1 Electromagnetic Fields
191(2)
C.2 Scalar Fields
193(2)
Appendix D A Summary of Important Results
195(5)
D.1 Differential Geometry
195(2)
D.2 General Relativity
197(1)
D.3 The 3+1 Decomposition
197(1)
D.4 The Equations of Gauss, Codazzi, Mainardi, and Ricci
198(1)
D.5 The ADM Equations
199(1)
D.6 Conformal Decompositions
199(1)
Appendix E Answers to Selected Problems
200(2)
References 202(10)
Index 212
Thomas W. Baumgarte is the William R. Kenan Jr. Professor of Physics at Bowdoin College in Brunswick, Maine. His work in numerical relativity and relativistic astrophysics has been recognized with prizes and fellowships from the Guggenheim Foundation, the Humboldt Foundation, the American Physical Society, and the Simons Foundation. Stuart Shapiro and he have previously co-authored the graduate-level text Numerical Relativity: Solving Einstein's Equations on the Computer (Cambridge, 2010). Stuart L. Shapiro is a Professor of Physics and Astronomy at the University of Illinois at Urbana-Champaign. He is a leading scientist in theoretical astrophysics and general relativity and has been awarded numerous prizes and honors for his research and teaching, including Sloan and Guggenheim fellowships, IBM Supercomputing awards, and the Hans A. Bethe Prize of the American Physical Society, where he was elected Fellow. Shapiro has published over 400 research papers and, in addition to his writing with Thomas Baumgarte, he is co-author of the classic text Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (1983).