Lecture Notes On The Global Stability Of The Minkowski Space
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Lecture Notes On The Global Stability Of The Minkowski Space
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Author : Francesco Nicolò
language : en
Publisher:
Release Date : 2000
Lecture Notes On The Global Stability Of The Minkowski Space written by Francesco Nicolò and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Generalized spaces categories.
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.
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity
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Author : Lydia Bieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-30
Extensions Of The Stability Theorem Of The Minkowski Space In General Relativity written by Lydia Bieri 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 2009-06-30 with Mathematics categories.
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. In particular, she assumes less decay in the power of $r$ and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A nontrivial solution of these equations is a curved spacetime with an electromagnetic field. To prove the existence of solutions to the Einstein-Maxwell equations, Zipser follows the argument and methodology introduced by Christodoulou and Klainerman. To generalize the original results, she needs to contend with the additional curvature terms that arise due to the presence of the electromagnetic field $F$; in her case the Ricci curvature of the spacetime is not identically zero but rather represented by a quadratic in the components of $F$. In particular the Ricci curvature is a constant multiple of the stress-energy tensor for $F$. Furthermore, the traceless part of the Riemann curvature tensor no longer satisfies the homogeneous Bianchi equations but rather inhomogeneous equations including components of the spacetime Ricci curvature. Therefore, the second part of this book focuses primarily on the derivation of estimates for the new terms that arise due to the presence of the electromagnetic field.
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.
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields
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Author : Piotr T. Chrusciel
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields written by Piotr T. Chrusciel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Stability Of Spherically Symmetric Wave Maps
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Author : Joachim Krieger
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Stability Of Spherically Symmetric Wave Maps written by Joachim Krieger 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 2006 with Mathematics categories.
Presents a study of Wave Maps from ${\mathbf{R}}^{2+1}$ to the hyperbolic plane ${\mathbf{H}}^{2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+\mu}$, $\mu>0$.
Handbook Of Quantum Gravity
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Author : Cosimo Bambi
language : en
Publisher: Springer Nature
Release Date : 2024-12-03
Handbook Of Quantum Gravity written by Cosimo Bambi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-03 with Science categories.
The search for a theory of quantum gravity is one of the most important and fascinating problems in modern theoretical physics. While we do not have yet a complete theory of quantum gravity, significant advancements have been done in the past decades. In this handbook, every section is dedicated to a specific approach towards a theory of quantum gravity and is edited by the leading experts in the field. This book represents both a valuable resource for graduate students and an important reference for researchers in quantum gravity.
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.
Global Lorentzian Geometry
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Author : John K. Beem
language : en
Publisher: Routledge
Release Date : 2017-09-29
Global Lorentzian Geometry written by John K. Beem and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-29 with Science categories.
Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.
2023 Matrix Annals
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Author : David R. Wood
language : en
Publisher: Springer Nature
Release Date : 2025-07-02
2023 Matrix Annals written by David R. Wood and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-02 with Mathematics categories.
MATRIX is Australia’s residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1–2 weeks in duration. This book is a scientific record of the 14 research programs held at MATRIX in 2023, including combined events with the Mathematisches Forschungsinstitut Oberwolfach (MFO), and with the Research Institute for Mathematical Sciences Kyoto University (RIMS).