Stability for Linearized Gravity on the Kerr SpacetimeStability for Linearized Gravity on the Kerr SpacetimeL. Andersson et al.

被引：0

作者：

Lars Andersson ^{[1
]}

Thomas Bäckdahl ^{[2
]}

Pieter Blue ^{[3
]}

Siyuan Ma ^{[4
]}

机构：

[1] Beijing Institute of Mathematical Sciences and Applications,Mathematical Sciences

[2] Chalmers University of Technology,Academy of Mathematics and Systems Science

[3] University of Gothenburg,undefined

[4] Maxwell Institute,undefined

[5] The University of Edinburgh,undefined

[6] Chinese Academy of Science,undefined

来源：

Annals of PDE | 2025年 / 11卷 / 1期

关键词：

D O I：

10.1007/s40818-024-00193-w

中图分类号：

学科分类号：

摘要：

In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full subextreme range of Kerr black holes, provided integrated energy estimates for the Teukolsky equation hold. For slowly rotating Kerr backgrounds, such estimates are known to hold, due to the work of one of the authors. The results in this paper thus provide the first stability results for linearized gravity on the Kerr background, in the slowly rotating case, and reduce the linearized stability problem for the full subextreme range to proving integrated energy estimates for the Teukolsky equation. This constitutes an essential step towards a proof of the black hole stability conjecture, i.e. the statement that the Kerr family is dynamically stable, one of the central open problems in general relativity.

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