QNM completeness for Kerr ringdown expansions

open Spectral / Scattering

Statement

Prove or refute a mathematically precise completeness statement for Kerr quasinormal modes plus tails in late-time expansions of wave or gravitational fields.

Mathematical prerequisites

Meromorphic continuation of resolvents; contour deformation; branch-cut analysis; asymptotic expansions for non-selfadjoint operators.

Why it matters

This is the clean mathematical version of the folklore claim that ringdown is 'a sum of QNMs'.

Completion criteria

A complete answer must define the function space, the notion of completeness or asymptotic completeness, and the tail remainder precisely.

Implications if solved

Would settle one of the central structural questions behind black-hole spectroscopy.

Last updated: 2026-04-05 · Edit on GitHub →