Construction of GCM hypersurfaces in perturbations of Kerr
Abstract
This is a follow-up of KS:Kerr1 on the general covariant modulated (GCM) procedure in perturbations of Kerr. In this paper, we construct GCM hypersurfaces, which play a central role in extending GCM admissible spacetimes in KS:main where decay estimates are derived in the context of nonlinear stability of Kerr family for |a| m. As in KS, the central idea of the construction of GCM hypersurfaces is to concatenate a 1--parameter family of GCM spheres of KS:Kerr1 by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in KS and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.
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