Introduction To 3 1 Numerical Relativity PDF Download
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| Author | : Miguel Alcubierre |
| Publisher | : OUP Oxford |
| Total Pages | : 464 |
| Release | : 2008-04-10 |
| Genre | : Science |
| ISBN | : 0191548294 |
Download Introduction to 3+1 Numerical Relativity Book 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.
| Author | : Éric Gourgoulhon |
| Publisher | : Springer |
| Total Pages | : 304 |
| Release | : 2012-02-27 |
| Genre | : Science |
| ISBN | : 3642245250 |
Download 3+1 Formalism in General Relativity Book 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.
| Author | : Thomas W. Baumgarte |
| Publisher | : Cambridge University Press |
| Total Pages | : 717 |
| Release | : 2010-06-24 |
| Genre | : Science |
| ISBN | : 1139643177 |
Download Numerical Relativity Book 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.
| Author | : Masaru Shibata |
| Publisher | : World Scientific |
| Total Pages | : 844 |
| Release | : 2015-11-05 |
| Genre | : Science |
| ISBN | : 981469973X |
Download Numerical Relativity Book in PDF, ePub and Kindle
"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 | : Thomas W. Baumgarte |
| Publisher | : Cambridge University Press |
| Total Pages | : 235 |
| Release | : 2021-04-08 |
| Genre | : Science |
| ISBN | : 1108945171 |
Download Numerical Relativity: Starting from Scratch Book 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.
| Author | : Thomas W. Baumgarte |
| Publisher | : Cambridge University Press |
| Total Pages | : 717 |
| Release | : 2010-06-24 |
| Genre | : Science |
| ISBN | : 052151407X |
Download Numerical Relativity Book in PDF, ePub and Kindle
Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.
| Author | : Carles Bona |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2009-07-24 |
| Genre | : Science |
| ISBN | : 3642011632 |
Download Elements of Numerical Relativity and Relativistic Hydrodynamics Book in PDF, ePub and Kindle
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 | : William D. McGlinn |
| Publisher | : JHU Press |
| Total Pages | : 228 |
| Release | : 2003-04-30 |
| Genre | : Science |
| ISBN | : 0801877733 |
Download Introduction to Relativity Book in PDF, ePub and Kindle
Special relativity is a cornerstone of the structure of all fundamental theories, and general relativity has blossomed from Einstein's original theory into a cutting-edge applied science. Applications of Einstein's field equations describe such phenomena as supermassive black holes at the center of galaxies, the spiraling paths of binary pulsars, gravitational lensing caused by massive compact halo objects (Macho's), and the possibility of detecting gravitational waves emitted in cataclysmic cosmic events. In Introduction to Relativity, physics teacher and researcher Bill McGlinn explains the fundamental concepts of Einstein's special and general theories of relativity. He describes the basic consequences of special relativity—length contraction and time dilation—and the enigma of the twin paradox, as well as the Doppler shift of light. Relativistic dynamics is contrasted to Newtonian dynamics, followed by a discussion of relativistic tensor fields, including those of the electromagnetic field and the energy-momentum density of fluids. After a study of Einstein's early attempt at incorporating the equivalence principle into physics, McGlinn presents the general theory of relativity, discussing the three classic tests of relativity: the deflection of light by a gravitational field; the precession of perihelia; and the gravitational redshift of light. He also discusses other important applications, such as the dynamics of orbiting gyroscopes, the properties of stellar interiors, and black holes. The book ends with a chapter on cosmology, which includes discussions of kinematics and dynamics of the famed Robertson-Walker metric, Hubble's constant, cosmological constant, and cosmic microwave background radiation. For anyone seeking a brief, clear overview of modern general relativity which emphasizes physics over mathematics, McGlinn's Introduction to Relativity is indispensable.
| Author | : Ray d'Inverno |
| Publisher | : Oxford University Press |
| Total Pages | : 512 |
| Release | : 2022-05-12 |
| Genre | : Science |
| ISBN | : 0192606573 |
Download Introducing Einstein's Relativity Book in PDF, ePub and Kindle
There is little doubt that Einstein's theory of relativity captures the imagination. Not only has it radically altered the way we view the universe, but the theory also has a considerable number of surprises in store. This is especially so in the three main topics of current interest that this book reaches, namely: black holes, gravitational waves, and cosmology. The main aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. Indeed, the book follows Einstein in that it introduces the theory very much from a physical point of view. After introducing the special theory of relativity, the basic field equations of gravitation are derived and discussed carefully as a prelude to first solving them in simple cases and then exploring the three main areas of application. This new edition contains a substantial extension content that considers new and updated developments in the field. Topics include coverage of the advancement of observational cosmology, the detection of gravitational waves from colliding black holes and neutron stars, and advancements in modern cosmology. Einstein's theory of relativity is undoubtedly one of the greatest achievements of the human mind. Yet, in this book, the author makes it possible for students with a wide range of abilities to deal confidently with the subject. Based on both authors' experience teaching the subject this is achieved by breaking down the main arguments into a series of simple logical steps. Full details are provided in the text and the numerous exercises while additional insight is provided through the numerous diagrams. As a result this book makes an excellent course for any reader coming to the subject for the first time while providing a thorough understanding for any student wanting to go on to study the subject in depth
| Author | : Katy Clough |
| Publisher | : Springer |
| Total Pages | : 207 |
| Release | : 2018-06-16 |
| Genre | : Science |
| ISBN | : 3319926721 |
Download Scalar Fields in Numerical General Relativity Book in PDF, ePub and Kindle
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.
