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Mode Stability for the Teukolsky Equation on Extremal and Subextremal Kerr Spacetimes

Published version
Peer-reviewed

Type

Article

Change log

Authors

Teixeira da Costa, R  ORCID logo  https://orcid.org/0000-0002-2567-3821

Abstract

We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on Kerr black hole spacetimes, both in the extremal and subextremal case. We also give a quantitative refinement of mode stability. As an immediate application, we show that the transmission and reflection coefficients of the scattering problem are bounded, independently of the specific angular momentum of the black hole, in any compact set of real frequencies excluding zero frequency and the superradiant threshold. While in the subextremal setting these results were known previously, the extremal case is more involved and has remained an open problem. Ours are the first results outside axisymmetry and could serve as a preliminary step towards understanding boundedness, scattering and decay properties of general solutions to the Teukolsky equation on extremal Kerr black holes.

Description

Keywords

gr-qc, gr-qc, math.AP

Journal Title

Communications in Mathematical Physics

Conference Name

Journal ISSN

0010-3616
1432-0916

Volume Title

378

Publisher

Springer Science and Business Media LLC
Sponsorship
Engineering and Physical Sciences Research Council (EP/L016516/1)
EPSRC (1992791)
EPSRC Grant EP/L016516/1