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Author : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 235 pages
File Size : 42,8 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 : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 717 pages
File Size : 51,6 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 : Miguel Alcubierre
Publisher : OUP Oxford
Page : 464 pages
File Size : 43,7 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 : Éric Gourgoulhon
Publisher : Springer
Page : 294 pages
File Size : 42,8 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 : Carles Bona,Carlos Palenzuela-Luque
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 40,9 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 : Carles Bona,Carlos Palenzuela-Luque,Carles Bona-Casas
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 52,7 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 : Mattias Blennow,Tommy Ohlsson
Publisher : Cambridge University Press
Page : 365 pages
File Size : 54,9 Mb
Release : 2021-12-09
Category : Science
ISBN : 9781316510674
A textbook-neutral problems-and-solutions book that complements any relativity textbook at advanced undergraduate or masters level.
Author : Katy Clough
Publisher : Springer
Page : 197 pages
File Size : 55,7 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 : Thomas W. Baumgarte
Publisher : Unknown
Page : 698 pages
File Size : 51,7 Mb
Release : 2010
Category : Einstein field equations
ISBN : 0511728425
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, this textbook develops the mathematical formalism from first principles, then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves.
Author : Masaru Shibata
Publisher : World Scientific
Page : 844 pages
File Size : 49,5 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 : Ray D'Inverno
Publisher : Unknown
Page : 378 pages
File Size : 47,6 Mb
Release : 1992
Category : Electronic
ISBN : OCLC:876043207
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 : Dwight L. James
Publisher : iUniverse
Page : 110 pages
File Size : 50,6 Mb
Release : 2002-03
Category : Poetry
ISBN : 9780595221912
The poetry of Relativity embraces love and sexuality from the perspective of happiness and pain, while addressing the subtleties of emotional ambiguity. This book breathes new life into the way sexuality is expressed in our relationships and the way love is often portrayed during our social maturation. It parallels the struggles of overcoming the misgivings of personal heartache while providing restoration for faith and trust.
Author : Bernard F. Schutz
Publisher : Cambridge University Press
Page : 396 pages
File Size : 52,7 Mb
Release : 1985-01-31
Category : Science
ISBN : 0521277035
This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth.
Author : Eric Poisson
Publisher : Cambridge University Press
Page : 253 pages
File Size : 55,6 Mb
Release : 2004-05-06
Category : Science
ISBN : 9781139451994
This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.