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.

• Contains 300 exercises to help readers master new material • Numerous illustrations, many in color, assist in visualizing geometric concepts and highlight the results of computer simulations • Covers applications to topics of current physical and astrophysical significance

### Contents

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.

### Reviews

'Numerical relativity has come of age in the last few years, and Baumgarte and Shapiro have produced the first textbook on the subject. And what a book this is! Sufficiently complete to be an encyclopedia, yet accessible enough to be a genuine learning manual, the book is exceedingly well written. It covers virtually all aspects of numerical relativity, from formalism to the most modern application, and it is replete with beautiful and helpful diagrams. The book will serve as a useful reference to the researcher, and a source of enlightenment to many a student.' Eric Poisson, University of Guelph

'Numerical relativity has come of age with a number of recent breakthroughs. 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

'Over the last five years, there have been impressive advances in numerical relativity. It has now become a central area in the fast growing field of gravitational wave physics. These tools have played an important role also in the theory of critical phenomena associated with gravitational collapse, loop quantum cosmology and the discussion of quantum black holes and black branes. The book by Baumgarte and Shapiro provides an excellent introduction to the subject covering both, mathematical aspects and numerical techniques. The authors are world leaders in numerical relativity and their contributions have shaped neutron star simulations, the new frontier of this field. 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 in numerical relativity and neighboring fields.' Abhay Ashtekhar, Director, Institute for Gravitation and the Cosmos, Pennsylvania State University

'Quiescent black holes are well understood, but until recently nobody could calculate how they behave when they collide with each other, or are in the process of formation. Recent breakthroughs make such computations possible - an advance that is crucially important for understanding galactic nuclei and gravitational waves. 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

' … a well-written overview that includes a brief introduction to general relativity … and tips on matter sources of a gravitational field … the authors aim to make Numerical Relativity useful as a graduate-level textbook and not just a reference. That feature, and the text's coverage of neutron stars, distinguishes it from the other comprehensive treatments of the subject … It is difficult to imagine that a book covering a field at the intersection of multiple disciplines could please all possible audiences. Nonetheless, Numerical Relativity hits the mark in its quite comprehensive coverage. It will be useful for practitioners in the field and especially to graduate students wishing to join them in this active and exciting area of research.' Physics Today

'… an interesting and valuable contribution to the literature on this subject.' Cern Courier