000			05919cam a2200553Mu 4500
001			on1224361222
003			OCoLC
005			20220908100224.0
006			m o d
007			cr |||||||||||
008			201128s2020 nju o ||| 0 eng d
040			_aEBLCP _beng _cEBLCP _dOCLCO _dUKAHL _dJSTOR _dEBLCP _dOCLCO _dOCLCF _dN$T _dIEEEE _dOCLCO
020			_a9780691218526 _q(electronic bk.)
020			_a0691218528 _q(electronic bk.)
029	1		_aAU@ _b000068507184
035			_a(OCoLC)1224361222
037			_a22573/ctv15qs7m5 _bJSTOR
037			_a9519791 _bIEEE
050		4	_aQB843.B55
082	0	4	_a523.8875 _223
049			_aMAIN
100	1		_aSzeftel, J�er�emie. _965722
245	1	0	_aGlobal Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations _h[electronic resource] : _b(ams-210).
260			_aPrinceton : _bPrinceton University Press, _c2020.
300			_a1 online resource (859 p.).
490	1		_aAnnals of Mathematics Studies ; _vv.398
500			_aDescription based upon print version of record.
505	0		_aCover -- 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		_a1.3.3 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		_a3.2.2 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		_a3.5.3 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			_aEssential 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			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aSchwarzschild black holes. _965723
650		0	_aPerturbation (Mathematics) _920231
650		6	_aPerturbation (Math�ematiques) _963699
650		7	_aPerturbation (Mathematics) _2fast _0(OCoLC)fst01058905 _920231
650		7	_aSchwarzschild black holes. _2fast _0(OCoLC)fst01749023 _965723
655		4	_aElectronic books. _93294
700	1		_aKlainerman, Sergiu. _965724
776	0	8	_iPrint version: _aSzeftel, J�er�emie _tGlobal Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations : (ams-210) _dPrinceton : Princeton University Press,c2020 _z9780691212432
830		0	_aAnnals of mathematics studies. _965725
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9519791
938			_aAskews and Holts Library Services _bASKH _nAH37884752
938			_aProQuest Ebook Central _bEBLB _nEBL6403713
938			_aEBSCOhost _bEBSC _n2583264
942			_cEBK
994			_a92 _bINTKS
999			_c81502 _d81502