Numerical Relativity: Solving Einstein's Equations on the Computer

EAN: 9780521514071
Published: 24/06/2010
Language: English

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.

Preface
Suggestions for using this book
1. General relativity preliminaries
2. The 3+1 decomposition of Einstein's equations
3. Constructing initial data
4. Choosing coordinates
the lapse and shift
5. Matter sources
6. Numerical methods
7. Locating black hole horizons
8. Spherically symmetric spacetimes
9. Gravitational waves
10. Collapse of collisionless clusters in axisymmetry
11. Recasting the evolution equations
12. Binary black hole initial data
13. Binary black hole evolution
14. Rotating stars
15. Binary neutron star initial data
16. Binary neutron star evolution
17. Binary black hole-neutron stars
initial data and evolution
18. Epilogue
Appendixes
References
Index.