Journal
ANNALS OF PDE
Volume 8, Issue 2, Pages -Publisher
SPRINGERNATURE
DOI: 10.1007/s40818-022-00132-7
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Funding
- NSF [DMS 180841]
- Simons [10011738]
- ERC [ERC-2016 CoG 725589 EPGR]
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This study is a follow-up of the construction of GCM spheres in perturbations of Kerr, aiming to establish its existence and introduce the definition of angular momentum.
This is a follow-up of our paper (Klainerman and Szeftel in Construction of GCM spheres in perturbations of Kerr, Accepted for publication in Annals of PDE) on the construction of general covariant modulated (GCM) spheres in perturbations of Kerr, which we expect to play a central role in establishing their nonlinear stability. We reformulate the main results of that paper using a canonical definition of l = 1 modes on a 2-sphere embedded in a 1+3 vacuum manifold. This is based on a new, effective, version of the classical uniformization theorem which allows us to define such modes and prove their stability for spheres with comparable metrics. The reformulation allows us to prove a second, intrinsic, existence theorem for GCM spheres, expressed purely in terms of geometric quantities defined on it. A natural definition of angular momentum for such GCM spheres is also introduced, which we expect to play a key role in determining the final angular momentum for general perturbations of Kerr.
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