# introduction to 3 1 numerical relativity international series of monographs on physics

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## Introduction To 3 1 Numerical Relativity

**Author :**Miguel Alcubierre

**ISBN :**9780199205677

**Genre :**Computers

**File Size :**54. 35 MB

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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

**Author :**Thomas W. Baumgarte

**ISBN :**9781139643177

**Genre :**Science

**File Size :**90. 7 MB

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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.

## 3 1 Formalism In General Relativity

**Author :**Éric Gourgoulhon

**ISBN :**9783642245251

**Genre :**Science

**File Size :**27. 56 MB

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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.

## The Principles Of Quantum Mechanics

**Author :**Paul Adrien Maurice Dirac

**ISBN :**0198520115

**Genre :**Philosophy

**File Size :**71. 34 MB

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The first edition of this work appeared in 1930, and its originality won it immediate recognition as a classic of modern physical theory. The fourth edition has been bought out to meet a continued demand. Some improvements have been made, the main one being the complete rewriting of the chapter on quantum electrodymanics, to bring in electron-pair creation. This makes it suitable as an introduction to recent works on quantum field theories.

## Numerical Relativity

**Author :**Masaru Shibata

**ISBN :**9789814699747

**Genre :**Science

**File Size :**51. 93 MB

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' 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'

## The Mathematical Theory Of Black Holes

**Author :**Subrahmanyan Chandrasekhar

**ISBN :**0198503709

**Genre :**Science

**File Size :**50. 23 MB

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Part of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.

## Scalar Fields In Numerical General Relativity

**Author :**Katy Clough

**ISBN :**9783319926728

**Genre :**Science

**File Size :**29. 80 MB

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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.

## Springer Handbook Of Spacetime

**Author :**Abhay Ashtekar

**ISBN :**9783642419928

**Genre :**Science

**File Size :**49. 69 MB

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The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.

## Relativistic Hydrodynamics

**Author :**Luciano Rezzolla

**ISBN :**9780191509919

**Genre :**Science

**File Size :**50. 32 MB

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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.

## Phase Space Methods For Degenerate Quantum Gases

**Author :**Bryan J. Dalton

**ISBN :**9780199562749

**Genre :**Science

**File Size :**33. 57 MB

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This is a text and reference book on phase space theory for post-graduate students and researchers in the fields of condensed matter, cold quantum gases, and quantum optics who already have a basic understanding of quantum theory. The aim of the book is to provide a theoretical framework for understanding the physics of degenerate quantum gases, which occur in all these fields. The phase space theory is outlined both in terms of a treatment involving separatesingle particle states or modes and in terms of a treatment involving quantum fields. The book contains detailed derivations of all the key results, includes chapters covering necessary backgroundmathematics, with many exercises being provided for readers who wish to check their understanding.