{"title":"Construction of GCM Hypersurfaces in Perturbations of Kerr","authors":"Dawei Shen","doi":"10.1007/s40818-023-00152-x","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(|a|\\ll m\\)</span>. 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.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-023-00152-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
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.