The global nonlinear stability of the Minkowski space by Demetrios Christodoulou

Cover of: The global nonlinear stability of the Minkowski space | Demetrios Christodoulou

Published by Princeton University Press in Princeton .

Written in English

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Subjects:

  • Space and time -- Mathematics.,
  • Generalized spaces.,
  • Nonlinear theories.

Edition Notes

Includes bibliographical references (p. 513-514).

Book details

StatementDemetrios Christodoulou and Sergiu Klainerman.
SeriesPrinceton mathematical series ;, 41
ContributionsKlainerman, Sergiu, 1950-
Classifications
LC ClassificationsQC173.59.S65 C57 1993
The Physical Object
Paginationix, 514 p. ;
Number of Pages514
ID Numbers
Open LibraryOL1713488M
ISBN 100691087776
LC Control Number92015664

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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.

The aim of this book is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, our work accomplishes the following goals: 1. It provides a constructive proof of global, smooth, nontrivial solutions to the Einstein-Vacuum equations, which look, in the large, like the Minkowski : Demetrios Christodoulou.

arXivv1 [gr-qc] 28 Dec The global nonlinear stability of Minkowski space. Einstein equations, f(R)–modified gravity, and Klein-Gordon fields Philippe G. LeFloch∗ and Yue Ma† December ∗Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique, Sorbonne.

The Global Nonlinear Stability of Minkowski Space for Self-Gravitating Massive Fields (Series in Applied and Computational Mathematics Book 3) - Kindle edition by Philippe G LeFloch, Yue Ma. Download it once and read it on your Kindle device, PC, phones or tablets.

Use features like bookmarks, note taking and highlighting while reading The Global Nonlinear Stability of Minkowski Space. 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. Global Nonlinear Stability of the Minkowski Space (PMS) by Demetrios Christodoulou, Sergiu Klainerman,Princeton University Press edition, in English.

Stability of Minkowski Space for Massless Einstein Page 5 of 9 Fig. 1 The projection of the support of f in the uncoupled problem coordinates on Minkowski space R3+1 (these form a well defined coordinate system on the quotient manifold R3+1/SO(3) away from the centre of spherical symmetry {r = 0}) and suppose f is a solution of the Vlasov equation (2) with respect to this.

Book Description: 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.

Table of Contents was published in The Global Nonlinear Stability of the Minkowski Space (PMS) on page v. [C-K] D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space, Princeton, NJ: Princeton Univ.

Press, Show bibtex @book {C-K, MRKEY = {}. 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 Cited by: This book consists of two independent works: Part I is "Solutions of the Einstein Vacuum Equations", by Lydia Bieri.

Part II is "Solutions of the Einstein-Maxwell Equations", by Nina Zipser. A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this paper, we prove the global nonlinear stability of Minkowski space in the context of the spacelike-characteristic Cauchy problem for Einstein vacuum equations.

Spacelike-characteristic initial data are posed on a compact 3-disk and on the future complete null hypersurface emanating from its boundary. Our result extends the seminal stability result for Minkowski space proved by Author: Olivier Graf.

His books include The Global Nonlinear Stability of the Minkowski Space (Princeton). Jérémie Szeftel is a CNRS senior researcher in mathematics at the Laboratoire Jacques-Louis Lions of Sorbonne Université in Paris. J ws-book9x6 Nonlinear stability of Minkowski space for self-gravitating massive elds LeFloch-Ma-Book page 2 2 Nonlinear stability of Minkowski space for self-gravitating massive elds and, especially, the coupling between wave and Klein-Gordon equations.

This method was rst outlined in [39; 41], together with references to earlier. Product Information. 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.

Christodoulou, Demetrios / Klainerman, Sergiu The Global Nonlinear Stability of the Minkowski Space (PMS). The global nonlinear stability of Minkowski space for the Einstein equations in the presence of a massive field Stabilité non linéaire globale de l'espace-temps de Minkowski pour les champs massifs Presented by Haïm Brézis.

THE GLOBAL NONLINEAR STABILITY OF MINKOWSKI SPACE FOR SELF-GRAVITATING MASSIVE FIELDS. The Wave-Klein-Gordon Model PHILIPPE G. LEFLOCH AND YUE MA Abstract. The Hyperboloidal Foliation Method (introduced by the authors in ) is ex-tended here and applied to the Einstein equations of general relativity.

Speci cally, we establish. The Global Nonlinear Stability of the Minkowski Space. (PMS) 作者: Demetrios Christodoulou / Sergiu Klainerman 出版社: Princeton University Press 出版年: 定价: USD 装帧: Hardcover ISBN: The global nonlinear stability of the Minkowski space Christodoulou, Demetrios Klainerman, Sergiu; Abstract.

Publication: The global nonlinear stability of the Minkowski space. Pub Date: Bibcode: .C Keywords: Space and time; Generalized spaces; Nonlinear Cited by: Given an initial data set for the vacuum Einstein equations which is suitably close to that of Minkowski space, the monumental work of Christodoulou—Klainerman guarantees the corresponding solution exists globally and asymptotically approaches the Minkowski solution.

The Global Nonlinear Stability Of Minkowski Space For Self-gravitating Massive Fields World Scientific | English | Oct | ISBN | pages | PDF | mb.

by Philippe G Lefloch (Author),‎ Yue Ma (Author) This book is devoted to the Einstein’s field equations of general relativity for self-gravitating massive scalar.

A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result.

In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior.

Plot: 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.

Minkowski space is shown to be globally stable as a solution to the Einstein–Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the “wave zone”, and then proving a small data semi-global existence result for the characteristic initial value problem for the massless Einstein–Vlasov system in this region.

An illustration of an open book. Books. An illustration of two cells of a film strip. Video. An illustration of an audio speaker. Audio An illustration of a " floppy disk. The global nonlinear stability of Minkowski space for self-gravitating massive fields.

The wave-Klein-Gordon model. Author of The Global Nonlinear Stability of the Minkowski Space, The Global Nonlinear Stability Of The Minkowski Space, and The Action Principle and Partial Differential Equations.

(Am), Volume /5(2). Demetrios Christodoulou (Greek: Δημήτριος Χριστοδούλου; born Octo ) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime of special relativity in the framework of general odoulou is a MacArthur Fellow.

The Global Nonlinear Stability of the Minkowski Space. Minkowski space is displayed to be stable globally as a solution to the Einstein-Vlasov system in the.

Rate this book. Clear rating. 1 of 5 The Global Nonlinear Stability of the Minkowski Space (Pms) by. Demetrios Christodoulou, The Global Nonlinear Stability Of The Minkowski Space by. Demetrios Christodoulou, Sergiu Klainerman.

it was ok avg rating — 3/5(2). The Global Nonlinear Stability of the Minkowski Space (PMS) Demetrios Christodoulou. 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.

A GLOBAL ANALYSIS PROOF OF THE STABILITY OF MINKOWSKI SPACE AND THE POLYHOMOGENEITY OF THE METRIC PETER HINTZ AND ANDRAS VASY Abstract. We rst give a new proof of the non-linear stability of the (3+1)-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation.

We then show that. "The book gives a new proof of the central part of the theorem of Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski spaceThe authors prove, working in terms of double null foliations, a nonlinear stability, or global existence for. The Hyperboloidal Foliation Method (introduced by the authors in ) is extended here and applied to the Einstein equations of general relativity.

Specifically, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields, while existing methods only apply to massless scalar fields. First of all, by analyzing the structure of the Einstein equations.

Moreover, for the sake of simplicity and coherence, we restrict ourselves to the Einstein vacuum equations in the asymptotically flat regime. Our main goal is to discuss the main mathematical methods behind the various local existence and uniqueness results, as well as those used in the proof of global nonlinear stability of the Minkowski space.

My research interest includes Partial differential equations and analysis with a focus on the study of nonlinear wave equations. I have been working on Cauchy problem for quasilinear wave equations, including breakdown criterion for Einstein vacuum equations, local well-posedness of solution for very rough data and global nonlinear stability of Minkowski space with cerntain matter fields.

The global stability of the Minkowski spacetime solution to the Einstein-nonlinear system in wave coordinates Speck, Jared, Analysis & PDE, Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension Moriyama, Kazunori, Differential and Integral Equations, The book of Choquet-Bruhat cited above; D.

Christodoulou, S. Klainerman, "The Global Nonlinear Stability of Minkowski Space" (Princeton, ); S. Klainerman, F. Nicolò, "The Evolution Problem in General Relativity" (Birkhäuser, ); D.

Christodoulou, "The Formation of Black Holes in General Relativity" (European Mathematical Society, ). We discuss solutions of the Einstein vacuum (EV) equations. We solve the Cauchy problem for more general, asymptotically flat initial data than in the pioneering work `The Global Nonlinear Stability of the Minkowski Space' of D.

Christodoulou and S. Klainerman or than in any other work. Moreover, we describe precisely the asymptotic behaviour.

found: His The global nonlinear stability of the Minkowski space, CIP t.p. (Demetrios Christodoulou) pub. info. (b. in Athens; Ph.D. in physics; Prof.

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