Numerical Relativity: Solving Einstein's Equations on the Computer

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Cambridge University Press, Jun 24, 2010 - Science - 698 pages
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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, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.
 

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Contents

The3+1 decompostion of Einsteins equations
23
Constructing initial data
54
the lapse and shift
98
Matter sources
123
Numerical methods
183
Locating black hole horizons
229
Spherically symmetric spacetimes
253
Gravitational waves
311
Rotating stars
459
Binary neutron star initial data
506
Binary neutron star evolution
533
initial data and evolution
562
Epilogue
596
B Solving the vector Laplacian
608
E PostNewtonian results
616
basic equations
629

Collapse of collisionless clusters in axisymmetry
352
Recasting the evolution equations
375
Binary black hole initial data
394
Binary black hole evolution
429
analytical results
637
References
647
Index
684
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About the author (2010)

Thomas W. Baumgarte is a Professor of Physics at Bowdoin College, and an Adjunct Professor of Physics at the University of Illinois at Urbana-Champaign. He received his Diploma (1993) and Doctorate (1995) from Ludwig-Maximilians-Universität, München, and held postdoctoral positions at Cornell University and the University of Illinois before joining the faculty at Bowdoin College. He is a recipient of a John Simon Guggenheim Memorial Foundation Fellowship. He has written over 65 research articles on a variety of topics in general relativity and relativistic astrophysics, including black holes and neutron stars, gravitational collapse, and more formal mathematical issues.

Stuart L. Shapiro is a Professor of Physics and Astronomy at the University of Illinois at Urbana-Champaign. He received his A.B. from Harvard (1969) and his Ph.D. from Princeton (1973). He has published over 335 research articles spanning many topics in general relativity and theoretical astrophysics and co-authored the widely used textbook Black Holes, White Dwarfs and Neutron Stars; The Physics of Compact Objects (John Wiley, 1983). In addition to numerical relativity, Shapiro has worked on the physics and astrophysics of black holes and neutron stars, relativistic hydrodynamics, magnetohydrodynamics and stellar dynamics, and the generation of gravitational waves. He is a recipient of an IBM Supercomputing Award, a Forefronts of Large-Scale Computation Award, an Alfred P. Snow Research Fellowship, a John Simon Guggenheim Memorial Foundation Fellowship, and several teaching citations. He has served on the editorial boards of The Astrophysical Journal Letters and Classical and Quantum Gravity. He was elected Fellow of both the American Physical Society and Institute of Physics (UK).

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