Kerr stability in the full subextremal range

In the present paper, we extend the results in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen from the slowly rotating regime $\mathrm{\mid }a\mathrm{\mid }\ll m$ to the full subextremal range $\mathrm{\mid }a\mathrm{\mid }<m$, thereby completing the proof of the Kerr stability conjecture. The restriction $\mathrm{\mid }a\mathrm{\mid }\ll m$ enters in fact only through the estimates for wave equations and for the Bianchi system established in \cite{GKS22}. To remove this restriction, we crucially rely on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the inhomogeneous scalar wave equation and for inhomogeneous Teukolsky equations on perturbations of Kerr with $\mathrm{\mid }a\mathrm{\mid }<m$. Additionally, some of the results of the present paper are proved in our companion paper \cite{Sze}.