The Evolution Problem In General Relativity
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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.
The Global Nonlinear Stability Of The Minkowski Space
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Author : Demetrios Christodoulou
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
The Global Nonlinear Stability Of The Minkowski Space written by Demetrios Christodoulou and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The Cauchy Problem In General Relativity
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Author : Hans Ringström
language : en
Publisher: European Mathematical Society
Release Date : 2009
The Cauchy Problem In General Relativity written by Hans Ringström 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 Mathematics categories.
The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.
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.
Thirteenth Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Astrophysics And Relativistic Field Theories Proceedings Of The Mg13 Meeting On General Relativity In 3 Volumes
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Author : Remo Ruffini
language : en
Publisher: World Scientific
Release Date : 2015-01-26
Thirteenth Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Astrophysics And Relativistic Field Theories Proceedings Of The Mg13 Meeting On General Relativity In 3 Volumes written by Remo Ruffini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-26 with Science categories.
The Marcel Grossmann Meetings seek to further the development of the foundations and applications of Einstein's general relativity by promoting theoretical understanding in the relevant fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. The meetings discuss recent developments in classical and quantum aspects of gravity, and in cosmology and relativistic astrophysics, with major emphasis on mathematical foundations and physical predictions, having the main objective of gathering scientists from diverse backgrounds for deepening our understanding of spacetime structure and reviewing the current state of the art in the theory, observations and experiments pertinent to relativistic gravitation. The range of topics is broad, going from the more abstract classical theory, quantum gravity, branes and strings, to more concrete relativistic astrophysics observations and modeling.The three volumes of the proceedings of MG13 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 33 morning plenary talks during 6 days, and 75 parallel sessions over 4 afternoons. Volume A contains plenary and review talks ranging from the mathematical foundations of classical and quantum gravitational theories including recent developments in string/brane theories, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics including such topics as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star and pulsar astrophysics. Volumes B and C include parallel sessions which touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, binary systems, radiative transfer, accretion disks, quasors, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, and cosmic rays and the history of general relativity.
Problems Of Collapse And Numerical Relativity
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Author : D. Bancel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems Of Collapse And Numerical Relativity written by D. Bancel 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.
Proceedings of the NATO Advanced Research Workshop, Toulouse, France, November 7-11, 1983
General Relativity And Relativistic Astrophysics Proceedings Of The 4th Canadian Conference
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Author : Gabor Kunstatter
language : en
Publisher: World Scientific
Release Date : 1992-02-28
General Relativity And Relativistic Astrophysics Proceedings Of The 4th Canadian Conference written by Gabor Kunstatter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-28 with categories.
This proceedings contains the talks delivered at plenary and parallel sessions by leading researchers in both classical and quantum general relativity and in astrophysics.
Einstein S Field Equations And Their Physical Implications
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Author : Bernd G. Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-18
Einstein S Field Equations And Their Physical Implications written by Bernd G. Schmidt 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 2000-02-18 with Mathematics categories.
This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.
3 1 Formalism In General Relativity
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Author : Éric Gourgoulhon
language : en
Publisher: Springer
Release Date : 2012-02-27
3 1 Formalism In General Relativity written by Éric Gourgoulhon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-27 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.
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
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Author : R.J. Gleiser
language : en
Publisher: CRC Press
Release Date : 1993-01-01
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 written by R.J. Gleiser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Science categories.
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.