Global Nonlinear Stability Of Minkowski Space For Spacelike Characteristic Initial Data
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Global Nonlinear Stability Of Minkowski Space For Spacelike Characteristic Initial Data
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Author : Olivier Graf
language : en
Publisher:
Release Date : 2025
Global Nonlinear Stability Of Minkowski Space For Spacelike Characteristic Initial Data written by Olivier Graf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Differential equations, Partial categories.
"We prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations"--Page 4 of cover
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 Global Nonlinear Stability Of Minkowski Space For Self Gravitating Massive Fields
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Author : Philippe G Lefloch
language : en
Publisher: World Scientific
Release Date : 2017-08-16
The Global Nonlinear Stability Of Minkowski Space For Self Gravitating Massive Fields written by Philippe G Lefloch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-16 with Science categories.
This book is devoted to the Einstein's field equations of general relativity for self-gravitating massive scalar fields. We formulate the initial value problem when the initial data set is a perturbation of an asymptotically flat, spacelike hypersurface in Minkowski spacetime. We then establish the existence of an Einstein development associated with this initial data set, which is proven to be an asymptotically flat and future geodesically complete spacetime.
Global Nonlinear Stability Of Schwarzschild Spacetime Under Polarized Perturbations
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Author : Sergiu Klainerman
language : en
Publisher: Princeton University Press
Release Date : 2020-12-15
Global Nonlinear Stability Of Schwarzschild Spacetime Under Polarized Perturbations written by Sergiu Klainerman 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 2020-12-15 with Mathematics categories.
Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jérémie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes—or Schwarzschild spacetimes—under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.
Conformal Methods In General Relativity
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Author : Juan A. Valiente Kroon
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-21
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 2016-07-21 with Mathematics categories.
A systematic and self-contained account, which adopts a geometric approach to study the solutions of Einstein's theory of gravity.
Jean Leray 99 Conference Proceedings
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Author : Maurice de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Jean Leray 99 Conference Proceedings written by Maurice de Gosson 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 2013-11-11 with Mathematics categories.
This volume contains papers presented at the first conference held to honor the memory of, arguably, the greatest mathematician of the twentieth century, Jean Leray. Contributors from all over the world have submitted their work to be included in this unique collection, and it reflects the esteem in which Jean Leray was, and still is held. The book is divided into five parts: hyperbolic systems and equations; symplectic mechanics and geometry; sheaves and spectral sequences; elliptic operators and index theory; and mathematical physics. This volume will appeal to all those who acknowledge the value of Jean Leray's work in general, and students and researchers interested in analysis, topology and geometry, mathematical physics, classical mechanics and fluid mechanics and dynamics in particular.
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.
The Large Scale Structure Of Space Time
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Author : S. W. Hawking
language : en
Publisher: Cambridge University Press
Release Date : 1975-02-27
The Large Scale Structure Of Space Time written by S. W. Hawking 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 1975-02-27 with Science categories.
Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Extended Abstracts 2021 2022
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Author : Duván Cardona
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Extended Abstracts 2021 2022 written by Duván Cardona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.
The Geometry Of Kerr Black Holes
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Author : Barrett O'Neill
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
The Geometry Of Kerr Black Holes written by Barrett O'Neill and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Science categories.
Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.