For all sub-extremal Kerr spacetimes |a|<M, angular elliptic estimates control the full linearised curvature by the extremal Teukolsky components up to lower-order terms.
Linear stability of Kerr black holes in the full subextremal range
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We prove, unconditionally, the linear stability of the Kerr family in the full subextremal range. On an analytic level, our proof is the same as that of our earlier paper in the slowly rotating case. The additional ingredients we use are, firstly, the mode stability result proved by Andersson, Whiting, and the first author and, secondly, computations related to the zero energy behavior of the linearized gauge-fixed Einstein equation in work by the second author.
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Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range $|a|<M$
For all sub-extremal Kerr spacetimes |a|<M, angular elliptic estimates control the full linearised curvature by the extremal Teukolsky components up to lower-order terms.