Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : : (AMS-210) / / Sergiu Klainerman, Jérémie Szeftel.
Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this que...
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Year of Publication: | 2020 |
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Klainerman, Sergiu, author. aut http://id.loc.gov/vocabulary/relators/aut Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / Sergiu Klainerman, Jérémie Szeftel. Princeton, NJ : Princeton University Press, [2020] ©2020 1 online resource (856 p.) : 13 b/w illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 210 Frontmatter -- Contents -- List of Figures -- Acknowledgments -- 1 Introduction -- 2 Preliminaries -- 3 Main Theorem -- 4 Consequences of the Bootstrap Assumptions -- 5 Decay Estimates for q (Theorem M1) -- 6 Decay Estimates for and (Theorems M2, M3) -- 7 Decay Estimates (Theorems M4, M5) -- 8 Initialization and Extension (Theorems M6, M7, M8) -- 9 GCM Procedure -- 10 Regge-Wheeler Type Equations -- A Appendix to Chapter 2 -- B Appendix to Chapter 8 -- C Appendix to Chapter 9 -- D Appendix to Chapter 10 -- Bibliography restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holesOne 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 27. Jan 2023) Perturbation (Mathematics). Schwarzschild black holes. MATHEMATICS / Geometry / Non-Euclidean. bisacsh Bianchi identities. Hawking mass. Kerr metric. Morawetz estimates. Reege-Wheeler equations. Ricci coefficients. Theorem M0. asymptotic stability. cosmic censorship. curvature components. decay estimates. extreme curvature components. general covariance. general null frame transformations. general theory of relativity. geometric analysis. invariant quantities. mathematical physics, differential geometry. molecular orbital theory. null structure. partial differential equations. polarized symmetry. space-time. Szeftel, Jérémie, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2020 9783110690088 print 9780691212425 https://doi.org/10.1515/9780691218526?locatt=mode:legacy https://www.degruyter.com/isbn/9780691218526 Cover https://www.degruyter.com/document/cover/isbn/9780691218526/original |
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English |
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author |
Klainerman, Sergiu, Klainerman, Sergiu, Szeftel, Jérémie, |
spellingShingle |
Klainerman, Sergiu, Klainerman, Sergiu, Szeftel, Jérémie, Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / Annals of Mathematics Studies ; Frontmatter -- Contents -- List of Figures -- Acknowledgments -- 1 Introduction -- 2 Preliminaries -- 3 Main Theorem -- 4 Consequences of the Bootstrap Assumptions -- 5 Decay Estimates for q (Theorem M1) -- 6 Decay Estimates for and (Theorems M2, M3) -- 7 Decay Estimates (Theorems M4, M5) -- 8 Initialization and Extension (Theorems M6, M7, M8) -- 9 GCM Procedure -- 10 Regge-Wheeler Type Equations -- A Appendix to Chapter 2 -- B Appendix to Chapter 8 -- C Appendix to Chapter 9 -- D Appendix to Chapter 10 -- Bibliography |
author_facet |
Klainerman, Sergiu, Klainerman, Sergiu, Szeftel, Jérémie, Szeftel, Jérémie, Szeftel, Jérémie, |
author_variant |
s k sk s k sk j s js |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Szeftel, Jérémie, Szeftel, Jérémie, |
author2_variant |
j s js |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Klainerman, Sergiu, |
title |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / |
title_sub |
(AMS-210) / |
title_full |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / Sergiu Klainerman, Jérémie Szeftel. |
title_fullStr |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / Sergiu Klainerman, Jérémie Szeftel. |
title_full_unstemmed |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / Sergiu Klainerman, Jérémie Szeftel. |
title_auth |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / |
title_alt |
Frontmatter -- Contents -- List of Figures -- Acknowledgments -- 1 Introduction -- 2 Preliminaries -- 3 Main Theorem -- 4 Consequences of the Bootstrap Assumptions -- 5 Decay Estimates for q (Theorem M1) -- 6 Decay Estimates for and (Theorems M2, M3) -- 7 Decay Estimates (Theorems M4, M5) -- 8 Initialization and Extension (Theorems M6, M7, M8) -- 9 GCM Procedure -- 10 Regge-Wheeler Type Equations -- A Appendix to Chapter 2 -- B Appendix to Chapter 8 -- C Appendix to Chapter 9 -- D Appendix to Chapter 10 -- Bibliography |
title_new |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : |
title_sort |
global nonlinear stability of schwarzschild spacetime under polarized perturbations : (ams-210) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2020 |
physical |
1 online resource (856 p.) : 13 b/w illus. |
contents |
Frontmatter -- Contents -- List of Figures -- Acknowledgments -- 1 Introduction -- 2 Preliminaries -- 3 Main Theorem -- 4 Consequences of the Bootstrap Assumptions -- 5 Decay Estimates for q (Theorem M1) -- 6 Decay Estimates for and (Theorems M2, M3) -- 7 Decay Estimates (Theorems M4, M5) -- 8 Initialization and Extension (Theorems M6, M7, M8) -- 9 GCM Procedure -- 10 Regge-Wheeler Type Equations -- A Appendix to Chapter 2 -- B Appendix to Chapter 8 -- C Appendix to Chapter 9 -- D Appendix to Chapter 10 -- Bibliography |
isbn |
9780691218526 9783110494914 9783110690088 9780691212425 |
callnumber-first |
Q - Science |
callnumber-subject |
QB - Astronomy |
callnumber-label |
QB843 |
callnumber-sort |
QB 3843 B55 |
url |
https://doi.org/10.1515/9780691218526?locatt=mode:legacy https://www.degruyter.com/isbn/9780691218526 https://www.degruyter.com/document/cover/isbn/9780691218526/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
520 - Astronomy |
dewey-ones |
523 - Specific celestial bodies & phenomena |
dewey-full |
523.8875 |
dewey-sort |
3523.8875 |
dewey-raw |
523.8875 |
dewey-search |
523.8875 |
doi_str_mv |
10.1515/9780691218526?locatt=mode:legacy |
oclc_num |
1233040511 |
work_keys_str_mv |
AT klainermansergiu globalnonlinearstabilityofschwarzschildspacetimeunderpolarizedperturbationsams210 AT szefteljeremie globalnonlinearstabilityofschwarzschildspacetimeunderpolarizedperturbationsams210 |
status_str |
n |
ids_txt_mv |
(DE-B1597)571622 (OCoLC)1233040511 |
carrierType_str_mv |
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hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2020 |
is_hierarchy_title |
Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (AMS-210) / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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