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arXiv · 2608.26034

Dual modes in Kerr spacetimes and the Whiting transform: Mode stability revisited

Oliver Petersen·András Vasy
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Abstract

The purpose of the paper is to place Whiting's classical growing mode stability argument, extended to real frequencies by Shlapentokh-Rothman for the scalar wave equation and by Andersson, Ma, Paganini and Whiting in general, in the framework of classical PDE theory. The key steps are: a description of the dual or adjoint modes, a singular phase space pairing argument which is technically executed via the Fourier transform, followed by a standard unique continuation result. One part of our description of the dual modes connects them directly to the standard mode solutions which are smooth over the event horizon. In the zero spin case, there is a geometric interpretation of this: quasinormal modes (for non-zero real frequencies) which are smooth across the future event horizon can be extended as distributional QNM solutions by 0 through the past event horizon. We also describe the behavior of mode solutions at the bifurcate sphere.

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Oliver Petersen, András Vasy. 2026-09-21. Dual modes in Kerr spacetimes and the Whiting transform: Mode stability revisited. https://arxiv.org/abs/2608.26034

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