Numerical Relativity: Starting from Scratch - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Relativity: Starting from Scratch write by Thomas W. Baumgarte. This book was released on 2021-04-08. Numerical Relativity: Starting from Scratch available in PDF, EPUB and Kindle. A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.
Numerical Relativity
Numerical Relativity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Relativity write by Thomas W. Baumgarte. This book was released on 2010-06-24. Numerical Relativity available in PDF, EPUB and Kindle. 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.
Numerical Relativity: Starting from Scratch
Numerical Relativity: Starting from Scratch - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Relativity: Starting from Scratch write by Thomas W. Baumgarte. This book was released on 2021-03-31. Numerical Relativity: Starting from Scratch available in PDF, EPUB and Kindle. Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.
3+1 Formalism in General Relativity
3+1 Formalism in General Relativity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook 3+1 Formalism in General Relativity write by Éric Gourgoulhon. This book was released on 2012-02-27. 3+1 Formalism in General Relativity available in PDF, EPUB and Kindle. 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.
Introduction to 3+1 Numerical Relativity
Introduction to 3+1 Numerical Relativity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to 3+1 Numerical Relativity write by Miguel Alcubierre. This book was released on 2008-04-10. Introduction to 3+1 Numerical Relativity available in PDF, EPUB and Kindle. This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction and numerical methods. There is also a final chapter with examples of some simple numerical space-times. The book is aimed at both graduate students and researchers in physics and astrophysics, and at those interested in relativistic astrophysics.
