Introduction To 3 1 Numerical Relativity

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Introduction To 3 1 Numerical Relativity

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Author : Miguel Alcubierre
language : en
Publisher: OUP Oxford
Release Date : 2008-04-10

Introduction To 3 1 Numerical Relativity written by Miguel Alcubierre and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-10 with Science categories.

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.

3 1 Formalism In General Relativity

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Author : Éric Gourgoulhon
language : en
Publisher: Springer
Release Date : 2012-02-27

3 1 Formalism In General Relativity written by Éric Gourgoulhon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-27 with Science categories.

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.

Numerical Relativity

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Author : Thomas W. Baumgarte
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24

Numerical Relativity written by Thomas W. Baumgarte and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Science categories.

Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.

Elements Of Numerical Relativity And Relativistic Hydrodynamics

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Author : Carles Bona
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-24

Elements Of Numerical Relativity And Relativistic Hydrodynamics written by Carles Bona and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-24 with Science categories.

Many large-scale projects for detecting gravitational radiation are currently being developed, all with the aim of opening a new window onto the observable Universe. As a result, numerical relativity has recently become a major field of research, and Elements of Numerical Relativity and Relativistic Hydrodynamics is a valuable primer for both graduate students and non-specialist researchers wishing to enter the field. A revised and significantly enlarged edition of LNP 673 Elements of Numerical Relativity, this book starts with the most basic insights and aspects of numerical relativity before it develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism; gauge, initial, and boundary conditions; and various numerical algorithms. And in addition to many revisions, it includes new, convenient damping terms for numerical implementations, a presentation of the recently-developed harmonic formalism, and an extensive, new chapter on matter space-times, containing a thorough introduction to relativistic hydrodynamics. While proper reference is given to advanced applications requiring large computational resources, most tests and applications in this book can be performed on a standard PC.

Elements Of Numerical Relativity

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Author : Carles Bona
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-07

Elements Of Numerical Relativity written by Carles Bona and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-07 with Science categories.

Spurred by the current development of numerous large-scale projects for detecting gravitational radiation, with the aim to open a completely new window to the observable Universe, numerical relativity has become a major field of research over the past years. Indeed, numerical relativity is the standard approach when studying potential sources of gravitational waves, where strong fields and relativistic velocities are part of any physical scenario. This book can be considered a primer for both graduate students and non-specialist researchers wishing to enter the field. Starting from the most basic insights and aspects of numerical relativity, Elements of Numerical Relativity develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism, gauge, initial and boundary conditions as well as various numerical algorithms. The tests and applications proposed in this book can be performed on a standard PC.

Numerical Relativity Starting From Scratch

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Author : Thomas W. Baumgarte
language : en
Publisher: Cambridge University Press
Release Date : 2021-04-08

Numerical Relativity Starting From Scratch written by Thomas W. Baumgarte and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-08 with Science categories.

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.

Relativity And Scientific Computing

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Author : Friedrich W Hehl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Relativity And Scientific Computing written by Friedrich W Hehl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

Numerical Relativity

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Author : Masaru Shibata
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016

Numerical Relativity written by Masaru Shibata and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.

This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.

Scalar Fields In Numerical General Relativity

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Author : Katy Clough
language : en
Publisher: Springer
Release Date : 2018-06-16

Scalar Fields In Numerical General Relativity written by Katy Clough and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-16 with Science categories.

This book explores the use of numerical relativity (NR) methods to solve cosmological problems, and describes one of the first uses of NR to study inflationary physics. NR consists in the solution of Einstein’s Equation of general relativity, which governs the evolution of matter and energy on cosmological scales, and in systems where there are strong gravitational effects, such as around black holes. To date, NR has mainly been used for simulating binary black hole and neutron star mergers like those detected recently by LIGO. Its use as a tool in fundamental problems of gravity and cosmology is novel, but rapidly gaining interest. In this thesis, the author investigates the initial condition problem in early universe cosmology – whether an inflationary expansion period could have “got going” from initially inhomogeneous conditions – and identifies criteria for predicting the robustness of particular models. State-of-the-art numerical relativity tools are developed in order to address this question, which are now publicly available.

Introducing Einstein S Relativity

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Author : Ray d'Inverno
language : en
Publisher: Oxford University Press, USA
Release Date : 2021-10

Introducing Einstein S Relativity written by Ray d'Inverno and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10 with Science categories.

This textbook provides students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject