Introduction To 3 1 Numerical Relativity

Author : Miguel Alcubierre
Publisher : OUP Oxford
Page : 464 pages
File Size : 42,7 Mb
Release : 2008-04-10
Category : Science
ISBN : 9780191548291

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Introduction to 3+1 Numerical Relativity by Miguel Alcubierre Pdf

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 : Miguel Alcubierre
Publisher : Oxford University Press
Page : 459 pages
File Size : 46,7 Mb
Release : 2008-04-10
Category : Computers
ISBN : 9780199205677

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Introduction to 3+1 Numerical Relativity by Miguel Alcubierre Pdf

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.

Author : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 235 pages
File Size : 43,9 Mb
Release : 2021-04-08
Category : Mathematics
ISBN : 9781108844116

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Numerical Relativity: Starting from Scratch by Thomas W. Baumgarte,Stuart L. Shapiro Pdf

A pedagogical and accessible introduction to numerical relativity, the key tool to model gravitational waves and black hole mergers.

Author : Masaru Shibata
Publisher : World Scientific
Page : 844 pages
File Size : 48,8 Mb
Release : 2015-11-05
Category : Science
ISBN : 9789814699747

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Numerical Relativity by Masaru Shibata Pdf

' 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'

Author : Thomas W. Baumgarte
Publisher : Unknown
Page : 698 pages
File Size : 54,5 Mb
Release : 2010
Category : Einstein field equations
ISBN : 0511728425

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Numerical Relativity by Thomas W. Baumgarte Pdf

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 : 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 : 9781139643177

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Numerical Relativity by Thomas W. Baumgarte,Stuart L. Shapiro Pdf

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 : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 717 pages
File Size : 53,9 Mb
Release : 2010-06-24
Category : Science
ISBN : 9780521514071

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Numerical Relativity by Thomas W. Baumgarte,Stuart L. Shapiro Pdf

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

Author : Joan M. Centrella
Publisher : CUP Archive
Page : 488 pages
File Size : 47,6 Mb
Release : 1986-09-18
Category : Science
ISBN : 0521328608

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Dynamical Spacetimes and Numerical Relativity by Joan M. Centrella Pdf

Author : Masaru Shibata
Publisher : World Scientific
Page : 844 pages
File Size : 41,9 Mb
Release : 2015-11-05
Category : Science
ISBN : 9789814699730

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Numerical Relativity by Masaru Shibata Pdf

"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 : Sergio Luigi Cacciatori,Alexander Kamenshchik
Publisher : Springer Nature
Page : 261 pages
File Size : 44,7 Mb
Release : 2023-03-15
Category : Mathematics
ISBN : 9783031218453

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Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity by Sergio Luigi Cacciatori,Alexander Kamenshchik Pdf

This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled “Einstein Equations: Physical and Mathematical Aspects of General Relativity”. Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: Quantum ergosphere General relativistic Poynting-Robertson effect modelling Numerical relativity Length-contraction in curved spacetime Classicality from an inhomogeneous universe Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

Author : Amol Sasane
Publisher : World Scientific
Page : 500 pages
File Size : 45,9 Mb
Release : 2021-08-10
Category : Science
ISBN : 9789811243790

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A Mathematical Introduction To General Relativity by Amol Sasane Pdf

The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.

Author : Ray D'Inverno
Publisher : Unknown
Page : 378 pages
File Size : 40,6 Mb
Release : 1992
Category : Science
ISBN : 0521439760

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Approaches to Numerical Relativity by Ray D'Inverno Pdf

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

Author : Katy Clough
Publisher : Springer
Page : 197 pages
File Size : 49,6 Mb
Release : 2018-06-16
Category : Science
ISBN : 9783319926728

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Scalar Fields in Numerical General Relativity by Katy Clough Pdf

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 : Nicholas J. Higham,Mark R. Dennis,Paul Glendinning,Paul A. Martin,Fadil Santosa,Jared Tanner
Publisher : Princeton University Press
Page : 1014 pages
File Size : 52,6 Mb
Release : 2015-09-09
Category : Mathematics
ISBN : 9780691150390

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Princeton Companion to Applied Mathematics by Nicholas J. Higham,Mark R. Dennis,Paul Glendinning,Paul A. Martin,Fadil Santosa,Jared Tanner Pdf

The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Author : Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea
Publisher : CRC Press
Page : 434 pages
File Size : 52,7 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9780203562338

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Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea Pdf

Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics cover