TY - JOUR
T1 - Kerr stability for small angular momentum
AU - Klainerman, Sergiu
AU - Szeftel, Jérémie
N1 - Funding Information:
The first author has been supported by the NSF grant DMS 1800841. He would like to thank the Laboratoire Jacques-Louis Lions and IHES for their hospitality during his many visits in Paris. The second author is supported by the ERC grant ERC-2016 CoG 725589 EPGR.
Publisher Copyright:
© 2023, International Press, Inc.. All rights reserved.
PY - 2023
Y1 - 2023
N2 - This is our main paper in which we prove the full, unconditional, nonlinear stability of the Kerr family Kerr(a,m) for small angular momentum, i.e. |a|/m« 1, in the context of asymptotically flat solutions of the Einstein vacuum equations (EVE). We rely on our GCM papers [40] and [41], the recently released [50], as well as on the general formalism contained in part I of [28], see also the older version in [27]. The recently released [28] also contains, in parts II, III, all hyperbolic type estimates needed in our work. Our work extends the strategy developed in [39], in which only axial polarized perturbations of Schwarzschild were treated, by developing new geometric and analytic ideas on how to deal with with general perturbations of Kerr. We note that the restriction to small angular momentum is needed only in [28], mainly for the Morawetz type estimates derived in that paper.
AB - This is our main paper in which we prove the full, unconditional, nonlinear stability of the Kerr family Kerr(a,m) for small angular momentum, i.e. |a|/m« 1, in the context of asymptotically flat solutions of the Einstein vacuum equations (EVE). We rely on our GCM papers [40] and [41], the recently released [50], as well as on the general formalism contained in part I of [28], see also the older version in [27]. The recently released [28] also contains, in parts II, III, all hyperbolic type estimates needed in our work. Our work extends the strategy developed in [39], in which only axial polarized perturbations of Schwarzschild were treated, by developing new geometric and analytic ideas on how to deal with with general perturbations of Kerr. We note that the restriction to small angular momentum is needed only in [28], mainly for the Morawetz type estimates derived in that paper.
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U2 - 10.4310/PAMQ.2023.v19.n3.a1
DO - 10.4310/PAMQ.2023.v19.n3.a1
M3 - Article
AN - SCOPUS:85167800331
SN - 1558-8599
VL - 19
SP - 791
EP - 1678
JO - Pure and Applied Mathematics Quarterly
JF - Pure and Applied Mathematics Quarterly
IS - 3
ER -