Clusters → Spectral / Scattering
Spectral / Scattering
Quasinormal modes, resolvents, inverse problems, scattering maps, pseudospectrum, and excitation factors.
27 problems 24 open 3 partial 0 needs review
By family (this cluster)
- Near-Kerr (vacuum) (22)
- Exact Kerr (3)
- Kerr–AdS (2)
By relevance
- Physics-facing (2)
- Mixed (5)
- Pure math (20)
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-603
Prove nonlinear stability of Kerr with quantitative scattering (asymptotic completeness near Kerr).
K-624
Prove a sharp characterization of near-extremal QNM clustering with explicit remainders.
K-625
Prove completeness/expansion of solutions in Kerr via QNMs plus branch-cut contributions (mathematical ringdown expansion).
K-627
Establish pseudospectrum bounds for Kerr wave operators and relate to transient growth near superradiance.
K-636
Prove sharp semiclassical quantization of Kerr QNMs with explicit high-frequency error bounds.
K-637
Prove rigorous existence and nonlinear stability/instability classification of Kerr-AdS endstates (black resonators/geons).
K-638
Prove nonlinear instability of Kerr-AdS in a theorem (beyond numerics/backreaction studies).
K-660
Establish a full nonlinear ringdown plus tail decomposition for near-Kerr vacuum spacetimes.
K-661
Determine whether QNM expansions are stable under small nonlinearities (nonlinear resonance theory).
K-662
Develop a rigorous theory of excitation factors in Kerr and prove universal bounds across (l,m).
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.