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Numerical Relativity: Solving Einstein's Equations on the Computer Hardcover – 24 Jun 2010


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'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

Book Description

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. The book contains 300 exercises, numerous illustrations (many in color), summary boxes, and applications to help readers master the subject.

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Amazon.com: 2 reviews
12 of 12 people found the following review helpful
Best introduction to ADM formalism 30 Jan. 2011
By A. Nelson - Published on Amazon.com
Format: Hardcover Verified Purchase
There are two aspects to this book, at least how I refer to it: an introduction to the ADM formalism, and numerical analysis of black hole physics.

As an introduction to the ADM formalism, it stands alone. Chapter 2 "The 3+1 decomposition of Einstein's equations" provides a very pedagogical introduction ranging from "How to foliate spacetime" to performing calculations. Maxwell's equations in 3+1 dimensions are used as a motivation. Then the notion of the Hamiltonian constraint and momentum constraints are introduced, with some intuition given.

Chapter 3 "Constructing Initial Data" discusses the York time-slicing (a.k.a. conformal transformations of the spatial metric) and how that affects the constraints --- the momentum constraint becomes messy, the Hamiltonian constraint becomes pretty. Mass, momentum, and angular momentum is discussed in light of the problems of coordinate independence.

I frequently refer this book to my friends who need to learn the ADM formalism, it is the best introduction to the subject. The numerical analysis is equally as delightful.

Beware, though, of minor typos (e.g. page 23, "The 3+1 decompostion[sic] of..."). The math appears to be correct, the reasoning justified. Just sparse spelling errors.
4 of 4 people found the following review helpful
Just what I needed 10 Mar. 2013
By M. Babiuc - Published on Amazon.com
Format: Hardcover Verified Purchase
I was looking for a book to use for my independent study students, and found this. It's well suited for my needs: interesting and easy enough to be self taught, it gets the job done!
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