The Global Nonlinear Stability of the Minkowski Space (PMS-41) / / Demetrios Christodoulou, Sergiu Klainerman.
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,...
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Superior document: | Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1980-1999 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2014] ©1994 |
Year of Publication: | 2014 |
Edition: | Course Book |
Language: | English |
Series: | Princeton Mathematical Series ;
153 |
Online Access: | |
Physical Description: | 1 online resource (526 p.) |
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LEADER | 09593nam a22020295i 4500 | ||
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001 | 9781400863174 | ||
003 | DE-B1597 | ||
005 | 20220131112047.0 | ||
006 | m|||||o||d|||||||| | ||
007 | cr || |||||||| | ||
008 | 220131t20141994nju fo d z eng d | ||
020 | |a 9781400863174 | ||
024 | 7 | |a 10.1515/9781400863174 |2 doi | |
035 | |a (DE-B1597)447505 | ||
035 | |a (OCoLC)979746759 | ||
040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
041 | 0 | |a eng | |
044 | |a nju |c US-NJ | ||
050 | 4 | |a QC173.59.S65 | |
072 | 7 | |a MAT012040 |2 bisacsh | |
082 | 0 | 4 | |a 530.1/1 |2 20 |
100 | 1 | |a Christodoulou, Demetrios, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 4 | |a The Global Nonlinear Stability of the Minkowski Space (PMS-41) / |c Demetrios Christodoulou, Sergiu Klainerman. |
250 | |a Course Book | ||
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2014] | |
264 | 4 | |c ©1994 | |
300 | |a 1 online resource (526 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a Princeton Mathematical Series ; |v 153 | |
505 | 0 | 0 | |t Frontmatter -- |t Table of Contents -- |t Acknowledgments -- |t CHAPTER 1. Introduction -- |t Part I. Preliminary Results in 2- and 3-Dimensional Riemannian Geometry -- |t CHAPTER 2. Generalized Hodge Systems in 2-D -- |t CHAPTER 3. General Results in 3-D Geometry -- |t CHAPTER 4. The Poisson Equation in 3-D -- |t CHAPTER 5. Curvature of an Initial Data Set -- |t CHAPTER 6. Deformation of 2-Surfaces in 3-D -- |t Part II. Bianchi Equations in Space-Time -- |t CHAPTER 7. The Comparison Theorem -- |t CHAPTER 8. The Error Estimates -- |t Part III. Construction of Global Space- Times. Proof of the Main Theorem -- |t CHAPTER 9. Construction of the Optical Function -- |t CHAPTER 10. Third Version of the Main Theorem -- |t CHAPTER 11. Second Fundamental Form -- |t CHAPTER 12. The Lapse Function -- |t CHAPTER 13. Derivatives of the Optical Function -- |t CHAPTER 14. The Last Slice -- |t CHAPTER 15. The Matching -- |t CHAPTER 16. The Rotation Vectorfields -- |t CHAPTER 17. Conclusions -- |t Bibliography |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a 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. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
650 | 0 | |a Generalized spaces. | |
650 | 0 | |a Nonlinear theories. | |
650 | 0 | |a Space and time |x Mathematics. | |
650 | 7 | |a MATHEMATICS / Geometry / Non-Euclidean. |2 bisacsh | |
653 | |a Angular momentum operator. | ||
653 | |a Asymptotic analysis. | ||
653 | |a Asymptotic expansion. | ||
653 | |a Big O notation. | ||
653 | |a Boundary value problem. | ||
653 | |a Cauchy-Riemann equations. | ||
653 | |a Coarea formula. | ||
653 | |a Coefficient. | ||
653 | |a Compactification (mathematics). | ||
653 | |a Comparison theorem. | ||
653 | |a Corollary. | ||
653 | |a Covariant derivative. | ||
653 | |a Curvature tensor. | ||
653 | |a Curvature. | ||
653 | |a Cut locus (Riemannian manifold). | ||
653 | |a Degeneracy (mathematics). | ||
653 | |a Degrees of freedom (statistics). | ||
653 | |a Derivative. | ||
653 | |a Diffeomorphism. | ||
653 | |a Differentiable function. | ||
653 | |a Eigenvalues and eigenvectors. | ||
653 | |a Eikonal equation. | ||
653 | |a Einstein field equations. | ||
653 | |a Equation. | ||
653 | |a Error term. | ||
653 | |a Estimation. | ||
653 | |a Euclidean space. | ||
653 | |a Existence theorem. | ||
653 | |a Existential quantification. | ||
653 | |a Exponential map (Lie theory). | ||
653 | |a Exponential map (Riemannian geometry). | ||
653 | |a Exterior (topology). | ||
653 | |a Foliation. | ||
653 | |a Fréchet derivative. | ||
653 | |a Geodesic curvature. | ||
653 | |a Geodesic. | ||
653 | |a Geodesics in general relativity. | ||
653 | |a Geometry. | ||
653 | |a Hodge dual. | ||
653 | |a Homotopy. | ||
653 | |a Hyperbolic partial differential equation. | ||
653 | |a Hypersurface. | ||
653 | |a Hölder's inequality. | ||
653 | |a Identity (mathematics). | ||
653 | |a Infinitesimal generator (stochastic processes). | ||
653 | |a Integral curve. | ||
653 | |a Intersection (set theory). | ||
653 | |a Isoperimetric inequality. | ||
653 | |a Laplace's equation. | ||
653 | |a Lie algebra. | ||
653 | |a Lie derivative. | ||
653 | |a Linear equation. | ||
653 | |a Linear map. | ||
653 | |a Logarithm. | ||
653 | |a Lorentz group. | ||
653 | |a Lp space. | ||
653 | |a Mass formula. | ||
653 | |a Mean curvature. | ||
653 | |a Metric tensor. | ||
653 | |a Minkowski space. | ||
653 | |a Nonlinear system. | ||
653 | |a Normal (geometry). | ||
653 | |a Null hypersurface. | ||
653 | |a Orthonormal basis. | ||
653 | |a Partial derivative. | ||
653 | |a Poisson's equation. | ||
653 | |a Projection (linear algebra). | ||
653 | |a Quantity. | ||
653 | |a Radial function. | ||
653 | |a Ricci curvature. | ||
653 | |a Riemann curvature tensor. | ||
653 | |a Riemann surface. | ||
653 | |a Riemannian geometry. | ||
653 | |a Riemannian manifold. | ||
653 | |a Sard's theorem. | ||
653 | |a Scalar (physics). | ||
653 | |a Scalar curvature. | ||
653 | |a Scale invariance. | ||
653 | |a Schwarzschild metric. | ||
653 | |a Second derivative. | ||
653 | |a Second fundamental form. | ||
653 | |a Sobolev inequality. | ||
653 | |a Sobolev space. | ||
653 | |a Stokes formula. | ||
653 | |a Stokes' theorem. | ||
653 | |a Stress-energy tensor. | ||
653 | |a Symmetric tensor. | ||
653 | |a Symmetrization. | ||
653 | |a Tangent space. | ||
653 | |a Tensor product. | ||
653 | |a Theorem. | ||
653 | |a Trace (linear algebra). | ||
653 | |a Transversal (geometry). | ||
653 | |a Triangle inequality. | ||
653 | |a Uniformization theorem. | ||
653 | |a Unit sphere. | ||
653 | |a Vector field. | ||
653 | |a Volume element. | ||
653 | |a Wave equation. | ||
653 | |a Weyl tensor. | ||
700 | 1 | |a Klainerman, Sergiu, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Legacy Lib. eBook Package 1980-1999 |z 9783110413441 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Legacy Lib. eBook Package Science |z 9783110413595 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Mathematical Series eBook Package |z 9783110501063 |o ZDB-23-PMS |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2014-2015 |z 9783110665925 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
776 | 0 | |c print |z 9780691603155 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9781400863174 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400863174 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400863174/original |
912 | |a 978-3-11-041344-1 Princeton Legacy Lib. eBook Package 1980-1999 |c 1980 |d 1999 | ||
912 | |a 978-3-11-041359-5 Princeton Legacy Lib. eBook Package Science | ||
912 | |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999 |c 1927 |d 1999 | ||
912 | |a 978-3-11-066592-5 Princeton University Press Complete eBook-Package 2014-2015 |c 2014 |d 2015 | ||
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