Global Aspects Of The Cauchy Problem In General Relativity
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Global Aspects Of The Cauchy Problem In General Relativity
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Author : Yvonne Choquet-Bruhat
language : en
Publisher:
Release Date : 1969
Global Aspects Of The Cauchy Problem In General Relativity written by Yvonne Choquet-Bruhat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
The Evolution Problem In General Relativity
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Author : Sergiu Klainerman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Evolution Problem In General Relativity written by Sergiu Klainerman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.
Einstein Equations Physical And Mathematical Aspects Of General Relativity
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Author : Sergio Cacciatori
language : en
Publisher: Springer Nature
Release Date : 2019-11-23
Einstein Equations Physical And Mathematical Aspects Of General Relativity written by Sergio Cacciatori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-23 with Science categories.
This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.
Mathematical Problems Of General Relativity I
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Author : Demetrios Christodoulou
language : en
Publisher: European Mathematical Society
Release Date : 2008
Mathematical Problems Of General Relativity I written by Demetrios Christodoulou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
Conformal Methods In General Relativity
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Author : Juan A. Valiente Kroon
language : en
Publisher: Cambridge University Press
Release Date : 2023-02-09
Conformal Methods In General Relativity written by Juan A. Valiente Kroon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
This 2016 volume, now reissued as OA, shows how conformal methods can be used to study Einstein's theory of gravity.
General Relativity And Gravitation Proceedings Of The 17th International Conference
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Author : Adrian Ottewill
language : en
Publisher: World Scientific
Release Date : 2005-11-07
General Relativity And Gravitation Proceedings Of The 17th International Conference written by Adrian Ottewill and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-07 with Science categories.
This authoritative volume provides a snapshot of the state of the art in gravitational physics and related mathematical fields, as well as a review of recent achievements and prospects for future work. With contributing authors among the world leaders in their respective fields, this proceedings volume is a worthy addition to this conference series, which constitutes one of the most important international meetings in the areas general relativity and gravitation.
3 1 Formalism In General Relativity
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Author : Éric Gourgoulhon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-29
3 1 Formalism In General Relativity written by Éric Gourgoulhon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-29 with Science categories.
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 Sixth Canadian Conference On General Relativity And Relativistic Astrophysics
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Author : Stephen Paul Braham
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
The Sixth Canadian Conference On General Relativity And Relativistic Astrophysics written by Stephen Paul Braham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Science categories.
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. It 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 discussed; and, invited talks given by researchers known for their ability to communicate their expertise.
Mathematical Aspects Of Classical Field Theory
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Author : Mark J. Gotay
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Mathematical Aspects Of Classical Field Theory written by Mark J. Gotay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
Classical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics.
The Formation Of Black Holes In General Relativity
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Author : Demetrios Christodoulou
language : en
Publisher: European Mathematical Society
Release Date : 2009
The Formation Of Black Holes In General Relativity written by Demetrios Christodoulou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Science categories.
In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity. Since that time a major challenge has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves. The theorems proved in this monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler-Lagrange equations of hyperbolic type and provides the means to tackle problems which have hitherto seemed unapproachable. This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations.