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Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations (Record no. 81502)

000 -LEADER
fixed length control field 05919cam a2200553Mu 4500
001 - CONTROL NUMBER
control field on1224361222
003 - CONTROL NUMBER IDENTIFIER
control field OCoLC
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20220908100224.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
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008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 201128s2020 nju o ||| 0 eng d
040 ## - CATALOGING SOURCE
Original cataloging agency EBLCP
Language of cataloging eng
Transcribing agency EBLCP
Modifying agency OCLCO
-- UKAHL
-- JSTOR
-- EBLCP
-- OCLCO
-- OCLCF
-- N$T
-- IEEEE
-- OCLCO
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780691218526
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0691218528
Qualifying information (electronic bk.)
029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC)
OCLC library identifier AU@
System control number 000068507184
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1224361222
037 ## - SOURCE OF ACQUISITION
Stock number 22573/ctv15qs7m5
Source of stock number/acquisition JSTOR
037 ## - SOURCE OF ACQUISITION
Stock number 9519791
Source of stock number/acquisition IEEE
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QB843.B55
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 523.8875
Edition number 23
049 ## - LOCAL HOLDINGS (OCLC)
Holding library MAIN
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Szeftel, J�er�emie.
9 (RLIN) 65722
245 10 - TITLE STATEMENT
Title Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
Medium [electronic resource] :
Remainder of title (ams-210).
260 ## - PUBLICATION, DISTRIBUTION, ETC.
Place of publication, distribution, etc. Princeton :
Name of publisher, distributor, etc. Princeton University Press,
Date of publication, distribution, etc. 2020.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (859 p.).
490 1# - SERIES STATEMENT
Series statement Annals of Mathematics Studies ;
Volume/sequential designation v.398
500 ## - GENERAL NOTE
General note Description based upon print version of record.
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title -- Copyright -- Contents -- List of Figures -- Acknowledgments -- 1 Introduction -- 1.1 Basic notions in general relativity -- 1.1.1 Spacetime and causality -- 1.1.2 The initial value formulation for Einstein equations -- 1.1.3 Special solutions -- 1.1.4 Stability of Minkowski space -- 1.1.5 Cosmic censorship -- 1.2 Stability of Kerr conjecture -- 1.2.1 Formal mode analysis -- 1.2.2 Vectorfield method -- 1.3 Nonlinear stability of Schwarzschild under polarized perturbations -- 1.3.1 Bare-bones version of our theorem -- 1.3.2 Linear stability of the Schwarzschild spacetime
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 1.3.3 Main ideas in the proof of Theorem 1.6 -- 1.3.4 Beyond polarization -- 1.3.5 Note added in proof -- 1.4 Organization -- 2 Preliminaries -- 2.1 Axially symmetric polarized spacetimes -- 2.1.1 Axial symmetry -- 2.1.2 Z-frames -- 2.1.3 Axis of symmetry -- 2.1.4 Z-polarized S-surfaces -- 2.1.5 Invariant S-foliations -- 2.1.6 Schwarzschild spacetime -- 2.2 Main equations -- 2.2.1 Main equations for general S-foliations -- 2.2.2 Null Bianchi identities -- 2.2.3 Hawking mass -- 2.2.4 Outgoing geodesic foliations -- 2.2.5 Additional equations -- 2.2.6 Ingoing geodesic foliation
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 3.2.2 Main norms in ^(int)M -- 3.2.3 Combined norms -- 3.2.4 Initial layer norm -- 3.3 Main theorem -- 3.3.1 Smallness constants -- 3.3.2 Statement of the main theorem -- 3.4 Bootstrap assumptions and first consequences -- 3.4.1 Main bootstrap assumptions -- 3.4.2 Control of the initial data -- 3.4.3 Control of averages and of the Hawking mass -- 3.4.4 Control of coordinates system -- 3.4.5 Pointwise bounds for higher order derivatives -- 3.4.6 Construction of a second frame in ^(ext)M -- 3.5 Global null frames -- 3.5.1 Extension of frames -- 3.5.2 Construction of the first global frame
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 3.5.3 Construction of the second global frame -- 3.6 Proof of the main theorem -- 3.6.1 Main intermediate results -- 3.6.2 End of the proof of the main theorem -- 3.6.3 Conclusions -- 3.7 The general covariant modulation procedure -- 3.7.1 Spacetime assumptions for the GCM procedure -- 3.7.2 Deformations of surfaces -- 3.7.3 Adapted frame transformations -- 3.7.4 GCM results -- 3.7.5 Main ideas -- 3.8 Overview of the proof of Theorems M0-M8 -- 3.8.1 Discussion of Theorem M0 -- 3.8.2 Discussion of Theorem M1 -- 3.8.3 Discussion of Theorem M2 -- 3.8.4 Discussion of Theorem M3
520 ## - SUMMARY, ETC.
Summary, etc. 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 J�er�emie 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.
590 ## - LOCAL NOTE (RLIN)
Local note IEEE
Provenance (VM) [OBSOLETE] IEEE Xplore Princeton University Press eBooks Library
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Schwarzschild black holes.
9 (RLIN) 65723
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Perturbation (Mathematics)
9 (RLIN) 20231
650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Perturbation (Math�ematiques)
9 (RLIN) 63699
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Perturbation (Mathematics)
Source of heading or term fast
Authority record control number or standard number (OCoLC)fst01058905
9 (RLIN) 20231
650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Schwarzschild black holes.
Source of heading or term fast
Authority record control number or standard number (OCoLC)fst01749023
9 (RLIN) 65723
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
9 (RLIN) 3294
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Klainerman, Sergiu.
9 (RLIN) 65724
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Szeftel, J�er�emie
Title Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (ams-210)
Place, publisher, and date of publication Princeton : Princeton University Press,c2020
International Standard Book Number 9780691212432
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Annals of mathematics studies.
9 (RLIN) 65725
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ieeexplore.ieee.org/servlet/opac?bknumber=9519791">https://ieeexplore.ieee.org/servlet/opac?bknumber=9519791</a>
938 ## -
-- Askews and Holts Library Services
-- ASKH
-- AH37884752
938 ## -
-- ProQuest Ebook Central
-- EBLB
-- EBL6403713
938 ## -
-- EBSCOhost
-- EBSC
-- 2583264
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type eBooks
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-- 92
-- INTKS

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