The Global Nonlinear Stability Of Minkowkski Space For Self Gravitating Massive Fields
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The Global Nonlinear Stability Of Minkowski Space For Self Gravitating Massive Fields
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Author : Lefloch Philippe G
language : en
Publisher: World Scientific
Release Date : 2017-08-16
The Global Nonlinear Stability Of Minkowski Space For Self Gravitating Massive Fields written by Lefloch Philippe G 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. Contents: IntroductionOverview of the Hyperboloidal Foliation MethodFunctional Analysis on Hyperboloids of Minkowski SpacetimeQuasi-Null Structure of the Einstein-Massive Field System on HyperboloidsInitialization of the Bootstrap ArgumentDirect Control of Nonlinearities in the Einstein EquationsDirect Consequences of the Wave Gauge ConditionSecond-Order Derivatives of the Spacetime MetricSup-Norm Estimate Based on CharacteristicsLow-Order Refined Energy Estimate for the Spacetime MetricLow-Order Refined Sup-Norm Estimate for the Metric and Scalar FieldHigh-Order Refined L² EstimatesHigh-Order Refined Sup-Norm EstimatesLow-Order Refined Energy Estimate for the Scalar FieldAppendices: Revisiting the Wave-Klein-Gordon ModelSup-Norm Estimate for the Wave EquationsSup-Norm Estimate for the Klein-Gordon EquationCommutator Estimates for the Hyperboloidal FrameBibliography Readership: Graduate students and researchers interested in mathematical general relativity. Keywords: General Relativity;Einstein Equations;Massive Field;Minkowski Space;Nonlinear Global Stability;Hyperboloidal Foliation MethodReview: Key Features: This is the first mathematical result on the global nonlinear stability of matter fields in general relativityProvide a framework to treat other matter fields such as the massive Yang-Mills fields which are of particular importance in physics
The Global Nonlinear Stability Of Minkowkski Space For Self Gravitating Massive Fields
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Author : Lefloch Philippe G
language : en
Publisher:
Release Date : 2018
The Global Nonlinear Stability Of Minkowkski Space For Self Gravitating Massive Fields written by Lefloch Philippe G and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Einstein field equations 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."--Publisher's website.
Theory Numerics And Applications Of Hyperbolic Problems Ii
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Author : Christian Klingenberg
language : en
Publisher: Springer
Release Date : 2018-06-27
Theory Numerics And Applications Of Hyperbolic Problems Ii written by Christian Klingenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-27 with Mathematics categories.
The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Developments In Lorentzian Geometry
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Author : Alma L. Albujer
language : en
Publisher: Springer Nature
Release Date : 2022-10-06
Developments In Lorentzian Geometry written by Alma L. Albujer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-06 with Mathematics categories.
This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Córdoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today. This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings. Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more. Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.
The Einstein Klein Gordon Coupled System
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Author : Alexandru D. Ionescu
language : en
Publisher: Princeton University Press
Release Date : 2022-03-15
The Einstein Klein Gordon Coupled System written by Alexandru D. Ionescu 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 2022-03-15 with Science categories.
A definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations This book provides a definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations of general relativity. Along the way, a novel robust analytical framework is developed, which extends to more general matter models. Alexandru Ionescu and Benoît Pausader prove global regularity at an appropriate level of generality of the initial data, and then prove several important asymptotic properties of the resulting space-time, such as future geodesic completeness, peeling estimates of the Riemann curvature tensor, conservation laws for the ADM tensor, and Bondi energy identities and inequalities. The book is self-contained, providing complete proofs and precise statements, which develop a refined theory for solutions of quasilinear Klein-Gordon and wave equations, including novel linear and bilinear estimates. Only mild decay assumptions are made on the scalar field and the initial metric is allowed to have nonisotropic decay consistent with the positive mass theorem. The framework incorporates analysis both in physical and Fourier space, and is compatible with previous results on other physical models such as water waves and plasma physics.
Global Existence Of Small Amplitude Solutions For A Model Quadratic Quasilinear Coupled Wave Klein Gordon System In Two Space Dimension With Mildly Decaying Cauchy Data
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Author : A. Stingo
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27
Global Existence Of Small Amplitude Solutions For A Model Quadratic Quasilinear Coupled Wave Klein Gordon System In Two Space Dimension With Mildly Decaying Cauchy Data written by A. Stingo and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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The Global Nonlinear Stability Of The Minkowski Space Pms 41
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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 Pms 41 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.
Hyperbolicity In Delay Equations
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Author : Luis Barreira
language : en
Publisher: World Scientific
Release Date : 2021-03-12
Hyperbolicity In Delay Equations written by Luis Barreira and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-12 with Mathematics categories.
This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms.The book is dedicated to researchers as well as graduate students specializing in differential equations and dynamical systems who wish to have an extensive and in-depth view of the hyperbolicity theory of delay equations. It can also be used as a basis for graduate courses on the stability and hyperbolicity of delay equations.
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.
Noncompact Problems At The Intersection Of Geometry Analysis And Topology
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Author : Abbas Bahri
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Noncompact Problems At The Intersection Of Geometry Analysis And Topology written by Abbas Bahri 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 2004 with Mathematics categories.
This proceedings volume contains articles from the conference held at Rutgers University in honor of Haim Brezis and Felix Browder, two mathematicians who have had a profound impact on partial differential equations, functional analysis, and geometry. Mathematicians attending the conference had interests in noncompact variational problems, pseudo-holomorphic curves, singular and smooth solutions to problems admitting a conformal (or some group) invariance, Sobolev spaces on manifolds, and configuration spaces. One day of the proceedings was devoted to Einstein equations and related topics. Contributors to the volume include, among others, Sun-Yung A. Chang, Luis A. Caffarelli, Carlos E. Kenig, and Gang Tian. The material is suitable for graduate students and researchers interested in problems in analysis and differential equations on noncompact manifolds.