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Author : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 717 pages
File Size : 54,8 Mb
Release : 2010-06-24
Category : Science
ISBN : 9780521514071
Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.
Author : Masaru Shibata
Publisher : World Scientific
Page : 844 pages
File Size : 51,7 Mb
Release : 2015-11-05
Category : Science
ISBN : 9789814699730
"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."--
Author : Carles Bona,Carlos Palenzuela-Luque,Carles Bona-Casas
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 44,9 Mb
Release : 2009-07-24
Category : Science
ISBN : 9783642011634
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.
Author : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 235 pages
File Size : 54,6 Mb
Release : 2021-04-08
Category : Mathematics
ISBN : 9781108844116
A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.
Author : Éric Gourgoulhon
Publisher : Springer
Page : 294 pages
File Size : 51,6 Mb
Release : 2012-02-27
Category : Science
ISBN : 9783642245251
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.
Author : Miguel Alcubierre
Publisher : OUP Oxford
Page : 464 pages
File Size : 48,5 Mb
Release : 2008-04-10
Category : Science
ISBN : 9780191548291
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.
Author : Carles Bona,Carlos Palenzuela-Luque
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 47,8 Mb
Release : 2005-07-07
Category : Science
ISBN : 3540257799
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.
Author : Katy Clough
Publisher : Springer
Page : 197 pages
File Size : 45,6 Mb
Release : 2018-06-16
Category : Science
ISBN : 9783319926728
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.
Author : Charles R. Evans,Lee Samuel Finn,David W. Hobill
Publisher : Cambridge University Press
Page : 451 pages
File Size : 45,5 Mb
Release : 1989-04-13
Category : Mathematics
ISBN : 9780521366663
This 1989 text will be of value to those who wish to understand developments in computer studies of general relativity at the time of publication.
Author : Joan M. Centrella
Publisher : CUP Archive
Page : 488 pages
File Size : 50,5 Mb
Release : 1986-09-18
Category : Science
ISBN : 0521328608
Author : D. Bancel,M. Signore
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400964600
Proceedings of the NATO Advanced Research Workshop, Toulouse, France, November 7-11, 1983
Author : James R. Wilson,Grant J. Mathews
Publisher : Cambridge University Press
Page : 234 pages
File Size : 54,8 Mb
Release : 2003-11-06
Category : Science
ISBN : 0521631556
Calculations of relativistic hydrodynamics are crucial to several areas of current research in the physics of supernovae and stellar collapse. This book provides an overview of the computational framework in which such calculations have been developed, with examples of applications to real physical systems. Beginning with the development of the equations and differencing schemes for special relativistic hydrodynamics, the book stresses the viability of the Euler-Lagrange approach to most astrophysical problems. It details aspects of solving the Einstein equations together with the fluid dynamics for various astrophysical systems in one, two and three dimensions.
Author : Friedrich W Hehl,Roland A. Puntigam,Hanns Ruder
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642957321
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.
Author : Luciano Rezzolla,Olindo Zanotti
Publisher : OUP Oxford
Page : 744 pages
File Size : 53,7 Mb
Release : 2013-09-26
Category : Science
ISBN : 9780191509919
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions). It is often said that fluids are either seen as solutions of partial differential equations or as "wet". Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.
Author : Jiří Bičák,Tomáš Ledvinka
Publisher : Springer
Page : 590 pages
File Size : 51,7 Mb
Release : 2014-06-06
Category : Science
ISBN : 9783319067612
In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper “Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham” in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", eds. J. Bičák and T. Ledvinka, published also by Springer Verlag.