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- TL;DR Summary
- Stability properties of Kerr BH's

Have these articles been discussed here previously? I could not find it but my search skills suck.

Recently (31th May this year)

Worth reading?

### Kerr stability for small angular momentum

https://arxiv.org/abs/2104.11857 (just 800 pages)This is our main paper in a series 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). Three papers in the series, \cite{KS-GCM1} and \cite{KS-GCM2} and \cite{GKS1} have already been released. We expect that the remaining ones \cite{GKS2}, \cite{KS:Kerr-B} and \cite{Shen} will appear shortly. Our work extends the strategy developed in \cite{KS}, 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 appears only in connection to Morawetz type estimates in \cite{GKS2} and \cite{KS:Kerr-B}

Recently (31th May this year)

### Wave equations estimates and the nonlinear stability of slowly rotating Kerr black holes

https://arxiv.org/abs/2205.14808 (just 900 pages)This is the last part of our proof of the nonlinear stability of the Kerr family for small angular momentum, i.e |a|/m≪1, in which we deal with the nonlinear wave type estimates needed to complete the project. More precisely we provide complete proofs for Theorems M1 and M2 as well the curvature estimates of Theorem M8, which were stated without proof in sections 3.7.1 and 9.4.7 of \cite{KS:Kerr}. Our procedure is based on a new general interest formalism (detailed in Part I of this work), which extends the one used in the stability of Minkowski space. Together with \cite{KS:Kerr} and the GCM papers \cite{KS-GCM1}, \cite{KS-GCM2}, \cite{Shen}, this work completes proof of the Main Theorem stated in Section 3.4 of \cite{KS:Kerr}.

Worth reading?