Clusters → Spectral / Scattering
Spectral / Scattering
Quasinormal modes, resolvents, inverse problems, scattering maps, pseudospectrum, and excitation factors.
18 problems 15 open 3 partial 0 needs review
By family (this cluster)
- Near-Kerr (vacuum) (15)
- Exact Kerr (3)
By relevance
- Physics-facing (2)
- Mixed (5)
- Pure math (11)
Taxonomy caveat. Cluster placement is a coarse editorial choice. Check each problem’s
family and asymptotics tags — e.g. Kerr–AdS and Kerr–de Sitter entries differ sharply from asymptotically
flat Kerr, even when they sit in “Exterior Stability” or “Interior / SCC”.
Filter the full database on the Problems page (family, asymptotics, FV suitability, …).
Problems in this cluster
K-401
QNM completeness for Kerr ringdown expansions
K-402
Nonlinear QNMs from full Einstein evolution
K-403
Scattering theory for linearized gravity on Kerr
K-404
Zero-frequency structure and tail universality
K-405
Inverse scattering for Kerr parameters
K-406
Spectral stability and pseudospectrum of Kerr QNMs
K-407
QNM excitation factors and universality theorems
K-504
Quantitative stability of the photon region and spherical null geodesics under near-Kerr perturbations
K-505
Threshold phenomena in separated Teukolsky-type ODEs on Kerr (zero modes, algebraically special limits, superradiant edges)
K-506
High-frequency Kerr quasinormal-mode laws with explicit remainder bounds
K-507
Finite-data inverse resonance recovery of Kerr parameters
K-661
Determine whether QNM expansions are stable under small nonlinearities (nonlinear resonance theory).
K-681
Develop a mathematically rigorous definition of nonlinear QNMs as poles of a suitable nonlinear response functional.
K-682
Prove that Kerr QNMs are stable under small perturbations of the metric in a topology relevant to stability proofs.
K-683
Prove a sharp characterization of the Kerr trapped set as a normally hyperbolic invariant manifold uniformly in a/M.
K-684
Prove that the linearized Einstein operator on Kerr has no embedded eigenvalues/resonances on the real axis beyond gauge.
K-688
Prove a fully rigorous PDE theorem for nonlinear superradiant instability of Kerr in a confining setting (mirror/AdS).
K-692
Prove sharp mapping properties of the Kerr scattering operator in weighted Sobolev spaces matching physical radiation norms.