Construction of GCM hypersurfaces in perturbations of Kerr. (English) Zbl 1524.35642

Shen, Dawei

Ann. PDE 9, No. 1, Paper No. 11, 112 p. (2023).

Summary: This is a follow-up of [5] 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 [7] where decay estimates are derived in the context of nonlinear stability of Kerr family for \(|a|\ll m\). As in [4], the central idea of the construction of GCM hypersurfaces is to concatenate a 1-parameter family of GCM spheres of [5] by solving an ODE system. The goal of this paper is to get rid of the symmetry restrictions in the GCM procedure introduced in [4] and thus remove an essential obstruction in extending the results to a full stability proof of the Kerr family.

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MSC:

35Q75

PDEs in connection with relativity and gravitational theory

Keywords:

frame transformations; GCM spheres; GCM hypersurfaces; Kerr stability

References:

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