Lecture Notes in Physics

3+1 Formalism in General Relativity

Bases of Numerical Relativity

Authors: Gourgoulhon, Éric

Free Preview
  • Introductory text based on lectures and graduate-level courses
  • Detailed derivations make this a self-contained and complete exposition of the subject matter
  • Authored by a leading experts in the field
see more benefits

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-24525-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA in USD
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.

Reviews

From the reviews:

“The monograph originating from lectures is devoted to the 3+1 formalism in general relativity. It starts with three chapters on basic differential geometry, the geometry of single hypersurfaces embedded in space-time, and the foliation of space-time by a family of spacelike hypersurfaces. … With the attempt to make the text self-consistent and complete, the calculations are … detailed such that the book is well suitable for undergraduate and graduate students.” (Horst-Heino von Borzeszkowski, Zentralblatt MATH, Vol. 1254, 2013)

“This book is written for advanced students and researchers who wish to learn the mathematical foundations of various approaches that have been proposed to solve initial value problems (with constraints) for the Einstein equations numerically. … Even for experts it may be useful, as it includes an extensive bibliography up to 2011.” (Hans-Peter Künzle, Mathematical Reviews, January, 2013)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-24525-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA in USD
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
3+1 Formalism in General Relativity
Book Subtitle
Bases of Numerical Relativity
Authors
Series Title
Lecture Notes in Physics
Series Volume
846
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-24525-1
DOI
10.1007/978-3-642-24525-1
Softcover ISBN
978-3-642-24524-4
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XVII, 294
Number of Illustrations
29 b/w illustrations
Topics