Stability for Linearized Gravity on the Kerr Spacetime
Artikel i vetenskaplig tidskrift, 2025

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.

Författare

Lars Andersson

Beijing Institute of Mathematical Sciences and Applications

Thomas Bäckdahl

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

P. Blue

Maxwell Institute for Mathematical Sciences

Siyuan Ma

Academy of Mathematics and System Sciences Chinese Academy of Sciences

Annals of PDE

25245317 (ISSN) 21992576 (eISSN)

Vol. 11 1 11

Ämneskategorier (SSIF 2025)

Beräkningsmatematik

Matematisk analys

Annan fysik

DOI

10.1007/s40818-024-00193-w

Mer information

Senast uppdaterat

2025-05-05