Scalar Fields In Numerical General Relativity

Author : Katy Clough
Publisher : Springer
Page : 197 pages
File Size : 48,7 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 : Thomas W. Baumgarte,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 235 pages
File Size : 45,7 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 : Alfredo Macías,Jorge L. Cervantes-Cota,Claus Lämmerzahl
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 49,6 Mb
Release : 2007-05-08
Category : Science
ISBN : 9780306471155

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Exact Solutions and Scalar Fields in Gravity by Alfredo Macías,Jorge L. Cervantes-Cota,Claus Lämmerzahl Pdf

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

Author : Miguel Alcubierre
Publisher : Oxford University Press
Page : 459 pages
File Size : 54,8 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 : Charles R. Evans,Lee Samuel Finn,David W. Hobill
Publisher : Cambridge University Press
Page : 451 pages
File Size : 43,9 Mb
Release : 1989-04-13
Category : Mathematics
ISBN : 9780521366663

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Frontiers in Numerical Relativity by Charles R. Evans,Lee Samuel Finn,David W. Hobill Pdf

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 : Sergio Luigi Cacciatori,Alexander Kamenshchik
Publisher : Springer Nature
Page : 261 pages
File Size : 40,7 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 : Carles Bona,Carlos Palenzuela-Luque,Carles Bona-Casas
Publisher : Springer
Page : 214 pages
File Size : 50,6 Mb
Release : 2009-07-14
Category : Science
ISBN : 9783642011641

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Elements of Numerical Relativity and Relativistic Hydrodynamics by Carles Bona,Carlos Palenzuela-Luque,Carles Bona-Casas Pdf

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 : M. A. H. MacCallum
Publisher : CUP Archive
Page : 440 pages
File Size : 40,9 Mb
Release : 1987-09-24
Category : Science
ISBN : 0521332966

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General Relativity and Gravitation by M. A. H. MacCallum Pdf

Author : Ray d'Inverno
Publisher : Cambridge University Press
Page : 402 pages
File Size : 40,7 Mb
Release : 1992-12-10
Category : Mathematics
ISBN : 9780521439763

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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 : Éric Gourgoulhon
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 46,5 Mb
Release : 2012-02-29
Category : Science
ISBN : 9783642245244

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3+1 Formalism in General Relativity by Éric Gourgoulhon Pdf

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,Stuart L. Shapiro
Publisher : Cambridge University Press
Page : 717 pages
File Size : 49,9 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 : R.J. Gleiser,C.N. Kozameh,O.M. Moreschi
Publisher : CRC Press
Page : 460 pages
File Size : 46,7 Mb
Release : 1993-01-01
Category : Science
ISBN : 0750302615

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General Relativity and Gravitation 1992, Proceedings of the Thirteenth INT Conference on General Relativity and Gravitation, held at Cordoba, Argentina, 28 June - July 4 1992 by R.J. Gleiser,C.N. Kozameh,O.M. Moreschi Pdf

General Relativity and Gravitation 1992 contains the best of 700 papers presented at the tri-annual INT conference, generally recognized as the key conference in the area. The plenary and invited papers are published in full, along with summaries of parallel symposia and workshops. The list of plenary speakers is as impressive as ever, with contributions from Jim Hartle, Roger Penrose, and Lee Smolin among many others.

Author : Piotr T. Chrusciel,Helmut Friedrich
Publisher : Birkhäuser
Page : 487 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034879538

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The Einstein Equations and the Large Scale Behavior of Gravitational Fields by Piotr T. Chrusciel,Helmut Friedrich Pdf

The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.

Author : David Hobill,Adrian Burd,A.A. Coley
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 50,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781475799934

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Deterministic Chaos in General Relativity by David Hobill,Adrian Burd,A.A. Coley Pdf

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

Author : Stephen Paul Braham,Jack David Gegenberg,Robert James McKellar
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 53,8 Mb
Release : 2024-06-02
Category : Science
ISBN : 082188588X

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The Sixth Canadian Conference on General Relativity and Relativistic Astrophysics by Stephen Paul Braham,Jack David Gegenberg,Robert James McKellar Pdf

This volume is the refereed proceedings of the Sixth Canadian Conference on General Relativity and Relativistic Astrophysics held in May 1995 at the University of New Brunswick. The book includes invited talks and contributed talks and posters including state-of-the art reviews of many of the most recent important developments in gravitational physics. This book would serve as a good supplement to standard texts on the topic. Features: * Review articles in key areas: black holes, numerical relativity, etc. * Contributions covering most of gravitational physics * Useful articles for students who wish to begin exploring the issues discusses * Invited talks given by researchers known for their ability to communicate their expertise