# Search Results for "introduction-to-3-1-numerical-relativity"

## Introduction to 3+1 Numerical Relativity

**Author**: Miguel Alcubierre**Publisher:**Oxford University Press**ISBN:**0199205671**Category:**Computers**Page:**444**View:**1066

This book is a self-contained introduction to the field of numerical relativity. Starting from basic general relativity, it introduces all the concepts and tools necessary for the fully relativistic simulation of astrophysical systems with strong and dynamical gravitational fields.

## Numerical Relativity

*Solving Einstein's Equations on the Computer*

**Author**: Thomas W. Baumgarte,Stuart L. Shapiro**Publisher:**Cambridge University Press**ISBN:**052151407X**Category:**Science**Page:**698**View:**6776

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

## 3+1 Formalism in General Relativity

*Bases of Numerical Relativity*

**Author**: Éric Gourgoulhon**Publisher:**Springer Science & Business Media**ISBN:**3642245242**Category:**Science**Page:**294**View:**5517

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

**Author**: Masaru Shibata**Publisher:**World Scientific**ISBN:**9814699748**Category:**Science**Page:**844**View:**4617

' 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. Contents:Preliminaries for Numerical RelativityMethodology:Formulation for Initial-Value Problems of General RelativityNumerical Methods for a Solution of Einstein''s Evolution EquationMatter Equations in General RelativityFormulations for Initial Data, Equilibrium, and Quasi-EquilibriumExtracting Gravitational WavesFinding Black HolesApplications:Coalescence of Binary Compact ObjectsGravitational Collapse to a Black HoleNon-Radial Instability and Magnetohydrodynamics InstabilityHigher-Dimensional SimulationsConclusionAppendices:Killing Vector and Frobenius'' TheoremNumerical Relativity in Spherical SymmetryDecomposition by Spherical HarmonicsLagrangian and Hamiltonian Formulations of General RelativitySolutions of Riemann Problems in Special Relativistic HydrodynamicsLandau–Lifshitz Pseudo TensorLaws of Black Hole and Apparent HorizonPost–Newtonian Results for Coalescing Compact Binaries Readership: This book is suitable for advanced ungraduate students, postgraduate students and researchers who are interested in numerical relativity. Keywords:Numerical Relativity;Black Hole;Neutron Star;Gravitational Waves'

## Approaches to Numerical Relativity

**Author**: Ray d'Inverno**Publisher:**Cambridge University Press**ISBN:**9780521017350**Category:**Science**Page:**400**View:**7564

Contributions by leading workers in the field given at an international workshop on Numerical Relativity held in Southampton in December 1991.

## Elements of Numerical Relativity

*From Einstein`s Equations to Black Hole Simulations*

**Author**: Carles Bona,Carlos Palenzuela-Luque**Publisher:**Springer Science & Business Media**ISBN:**9783540257790**Category:**Science**Page:**152**View:**3261

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.

## Relativistic Hydrodynamics

**Author**: Luciano Rezzolla,Olindo Zanotti**Publisher:**OUP Oxford**ISBN:**0191509914**Category:**Science**Page:**744**View:**1570

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.

## Elements of Numerical Relativity and Relativistic Hydrodynamics

*From Einstein' s Equations to Astrophysical Simulations*

**Author**: Carles Bona,Carlos Palenzuela-Luque,Carles Bona-Casas**Publisher:**Springer Science & Business Media**ISBN:**3642011632**Category:**Science**Page:**214**View:**6112

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.

## Special Relativity in General Frames

*From Particles to Astrophysics*

**Author**: Eric Gourgoulhon**Publisher:**Springer Science & Business Media**ISBN:**3642372767**Category:**Science**Page:**784**View:**9900

Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn’t restrict itself to inertial frames but considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. “A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Éric Gourgoulhon.” (excerpt from the Foreword by Thibault Damour)

## Numerical Methods in Astrophysics

*An Introduction*

**Author**: Peter Bodenheimer,Gregory P. Laughlin,Michal Rozyczka,Tomasz Plewa,Harold. W Yorke,Harold W. Yorke**Publisher:**CRC Press**ISBN:**9780750308830**Category:**Science**Page:**344**View:**3532

Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations. This resource indicates which methods are most suitable for particular problems, demonstrates what the accuracy requirements are in numerical simulations, and suggests ways to test for and reduce the inevitable negative effects. After an introduction to the basic equations and derivations, the book focuses on practical applications of the numerical methods. It explores hydrodynamic problems in one dimension, N-body particle dynamics, smoothed particle hydrodynamics, and stellar structure and evolution. The authors also examine advanced techniques in grid-based hydrodynamics, evaluate the methods for calculating the gravitational forces in an astrophysical system, and discuss specific problems in grid-based methods for radiation transfer. The book incorporates brief user instructions and a CD-ROM of the numerical codes, allowing readers to experiment with the codes to suit their own needs. With numerous examples and sample problems that cover a wide range of current research topics, this highly practical guide illustrates how to solve key astrophysics problems, providing a clear introduction for graduate and undergraduate students as well as researchers and professionals.

## A Relativist's Toolkit

*The Mathematics of Black-Hole Mechanics*

**Author**: Eric Poisson**Publisher:**Cambridge University Press**ISBN:**9781139451994**Category:**Science**Page:**N.A**View:**9827

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.

## Problem Book in Relativity and Gravitation

**Author**: Alan P. Lightman,William H. Press,Richard H. Price,Saul A. Teukolsky**Publisher:**Princeton University Press**ISBN:**1400889014**Category:**Science**Page:**616**View:**6941

An essential resource for learning about general relativity and much more, from four leading experts Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds. In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity.

## Advanced General Relativity

**Author**: John Stewart**Publisher:**Cambridge University Press**ISBN:**9780521449465**Category:**Science**Page:**228**View:**7415

A self-contained introduction to advanced general relativity.

## Introduction to Computational Physics for Undergraduates

**Author**: Omair Zubairi,Fridolin Weber**Publisher:**Morgan & Claypool Publishers**ISBN:**1681748959**Category:**Science**Page:**141**View:**2030

This is an introductory textbook on computational methods and techniques intended for undergraduates at the sophomore or junior level in the fields of science, mathematics, and engineering. It provides an introduction to programming languages such as FORTRAN 90/95/2000 and covers numerical techniques such as differentiation, integration, root finding, and data fitting. The textbook also entails the use of the Linux/Unix operating system and other relevant software such as plotting programs, text editors, and mark up languages such as LaTeX. It includes multiple homework assignments.

## An Introduction to General Relativity and Cosmology

**Author**: Jerzy Plebanski,Andrzej Krasinski**Publisher:**Cambridge University Press**ISBN:**113945840X**Category:**Science**Page:**N.A**View:**7197

General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.

## Spacetime Physics

**Author**: Edwin F. Taylor,John Archibald Wheeler**Publisher:**Macmillan**ISBN:**9780716723271**Category:**Science**Page:**312**View:**1150

Written by two of the field's true pioneers, Spacetime Physics can extend and enhance coverage of specialty relativity in the classroom. This thoroughly up-to-date, highly accessible overview covers microgravity, collider accelerators, satellite probes, neutron detectors, radioastronomy, and pulsars. The chapter on general relativity with new material on gravity waves, black holes, and cosmology.

## Principles of Cosmology and Gravitation

**Author**: Michael V Berry**Publisher:**Routledge**ISBN:**1351421905**Category:**Science**Page:**179**View:**4117

General relativity and quantum mechanics have become the two central pillars of theoretical physics. Moreover, general relativity has important applications in astrophysics and high-energy particle physics. Covering the fundamentals of the subject, Principles of Cosmology and Gravitation describes the universe as revealed by observations and presents a theoretical framework to enable important cosmological formulae to be derived and numerical calculations performed. Avoiding elaborate formal discussions, the book presents a practical approach that focuses on the general theory of relativity. It examines different evolutionary models and the gravitational effects of massive bodies. The book also includes a large number of worked examples and problems, half with solutions.

## A First Course in General Relativity

**Author**: Bernard Schutz**Publisher:**Cambridge University Press**ISBN:**0521887054**Category:**Science**Page:**393**View:**2602

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

## It's About Time

*Understanding Einstein's Relativity*

**Author**: N. David Mermin**Publisher:**Princeton University Press**ISBN:**1400830842**Category:**Science**Page:**208**View:**8389

In It's About Time, N. David Mermin asserts that relativity ought to be an important part of everyone's education--after all, it is largely about time, a subject with which all are familiar. The book reveals that some of our most intuitive notions about time are shockingly wrong, and that the real nature of time discovered by Einstein can be rigorously explained without advanced mathematics. This readable exposition of the nature of time as addressed in Einstein's theory of relativity is accessible to anyone who remembers a little high school algebra and elementary plane geometry. The book evolved as Mermin taught the subject to diverse groups of undergraduates at Cornell University, none of them science majors, over three and a half decades. Mermin's approach is imaginative, yet accurate and complete. Clear, lively, and informal, the book will appeal to intellectually curious readers of all kinds, including even professional physicists, who will be intrigued by its highly original approach.

## Physical Relativity

*Space-time Structure from a Dynamical Perspective*

**Author**: Harvey R. Brown**Publisher:**Oxford University Press on Demand**ISBN:**0199275831**Category:**Science**Page:**225**View:**2381

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein'streatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines andextends these arguments (which support a more 'constructive' approach to relativistic effects in Einstein's terminology), after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with therole this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory withquantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics.