Quasinormal modes for the Kerr black hole

TL;DR

This paper rigorously defines quasinormal modes for Kerr black holes as poles of a meromorphically continued resolvent, using complex scaling and microlocal analysis, and studies their distribution across energy regimes.

Contribution

It introduces a rigorous mathematical framework for Kerr black hole quasinormal modes and analyzes their spectral distribution using advanced analytical techniques.

Findings

Existence of a high energy spectral gap.

No accumulation of modes at zero energy.

Distribution analysis of modes in different energy regimes.

Abstract

We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near asymptotically flat infinity with microlocal methods near the black hole horizon. We study the distribution of quasinormal modes in both the high and low energy regimes. We establish the existence of a high energy spectral gap and exclude the accumulation of quasinormal modes at zero energy.