Clusters → Exterior Stability
Exterior Stability
Global exterior dynamics, decay, scattering, and radiation for near-Kerr spacetimes. Includes the main Kerr stability conjecture and its extensions to matter fields and near-extremal regimes.
61 problems 46 open 11 partial 2 needs review
By family (this cluster)
- Near-Kerr (vacuum) (48)
- Kerr–Newman (5)
- Related rotating BH (4)
- Kerr–de Sitter (3)
- Kerr–AdS (1)
By relevance
- Pure math (57)
- Mixed (1)
- Physics-facing (3)
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-001
Full nonlinear stability of subextremal Kerr
K-002
Uniform nonlinear stability as $a \to M^-$
K-003
Nonlinear asymptotic completeness near Kerr
K-004
Peeling and polyhomogeneous expansions at null infinity for nonlinear near-Kerr evolutions
K-005
Sharp nonlinear Price law for curvature
K-006
Kerr stability with BMS charges and nonlinear memory
K-007
Einstein–Maxwell stability near Kerr
K-008
Full asymptotically flat stability of the subextremal Kerr–Newman family
K-009
Einstein–massive Klein–Gordon near Kerr: classification of stable and unstable regimes
K-010
Nonlinear superradiant endstates in Kerr–AdS
K-011
Spin fields on dynamical near-Kerr backgrounds
K-012
Low-regularity Kerr stability threshold
K-013
Formation plus relaxation to Kerr
K-014
Nonlinear decay versus resonance expansions
K-601
Prove unconditional linear stability of Kerr (full subextremal range) in a fixed gauge, with full decay rates.
K-602
Prove nonlinear stability of Kerr for the full subextremal range |a|<M.
K-604
Establish a sharp peeling/polyhomogeneity theorem at future null infinity ($\mathcal{I}^+$) for nonlinear near-Kerr evolutions.
K-605
Prove sharp nonlinear Price-law tails for curvature in near-Kerr vacuum.
K-606
Prove Kerr-Newman linear stability for a wider parameter regime beyond weak charge/slow rotation.
K-607
Prove nonlinear stability of Kerr-Newman in the asymptotically flat setting (full coupling).
K-608
Prove unconditional nonlinear stability of slowly rotating Kerr-de Sitter.
K-609
Prove conditional nonlinear stability of Kerr-de Sitter in the full subextremal range under explicit mode-stability assumptions.
K-612
Prove generic sharp lower bounds on event-horizon flux for spin-2 Teukolsky fields.
K-616
Prove robust control of trapping geometry under dynamical near-Kerr perturbations in a sharp topology.
K-628
Derive rigorous late-time tail constants for scalar wave on Kerr in full subextremal range.
K-629
Prove robust decay estimates for Maxwell/Dirac fields on Kerr without small-a restriction, in sharp norms.
K-630
Prove nonlinear stability of Schwarzschild without codimension restrictions (full moduli convergence to Kerr).
K-632
Quantify how much Kerrness can be certified from finite-radius curvature invariants (numerical-relativity certification).
K-635
Establish quantitative stability of photon regions for small metric perturbations in Ck/Sobolev norms.
K-639
Classify superradiant instability windows for massive scalar fields on Kerr in fully rigorous parameter inequalities.
K-640
Prove nonlinear outcomes of Einstein-Klein-Gordon near Kerr in regimes with linear superradiant instability.
K-642
Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.
K-649
Formalize in a proof assistant: the exact Kerr separability structure and Carter constant derivation.
K-650
Formalize: equivalence of Teukolsky and Regge-Wheeler transformations in Schwarzschild and slowly rotating Kerr.
K-651
Prove linear stability of Kerr in alternative gauges (radiation gauges, generalized wave gauges) with explicit gauge maps.
K-652
Prove nonlinear stability of Kerr under weaker asymptotic flatness (polyhomogeneous/rough null infinity assumptions).
K-653
Establish sharp decay for Teukolsky equation on Kerr in full range with quantitative constants usable as blackboxes.
K-655
Prove explicit sharp late-time asymptotics for scalar field along the event horizon in Kerr (full range).
K-659
Prove sharp resolvent bounds near omega=0 for Kerr linearized Einstein operator, uniform in a/M.
K-663
Prove stability of the photon sphere/trapped set for families of metrics satisfying Einstein vacuum approximately.
K-664
Prove robust decay estimates for wave/Teukolsky equations on perturbed Kerr backgrounds without separability.
K-665
Prove quantitative mode stability for Kerr-de Sitter in full subextremal range and feed into nonlinear stability.
K-669
Prove global existence and weak cosmic censorship for small perturbations of Kerr data in an appropriate gauge.
K-670
Prove existence of trapped surfaces in vacuum from very low regularity characteristic data.
K-671
Derive sharp stability thresholds for massive fields on Kerr: identify stable/unstable mass windows with proofs.
K-672
Prove that generic small perturbations of Kerr generate nonzero angular momentum in the asymptotic Kerr parameter (modulation).
K-673
Prove a quantitative angular-momentum extraction formula from $\mathcal{I}^+$ radiation for near-Kerr vacuum spacetimes.
K-674
Prove that near-Kerr spacetimes admit a robust foliation by generalized GCM spheres with quantified control.
K-676
Prove sharp bounds on superradiant amplification for waves on Kerr uniform in a/M.
K-677
Prove stability of Kerr under small non-vacuum perturbations (e.g., Einstein-Vlasov) in a near-Kerr regime.
K-678
Prove nonlinear stability of Kerr under polarized symmetry-breaking perturbations (intermediate symmetry classes).
K-679
Prove stability/instability of higher-dimensional Kerr (Myers-Perry) in PDE sense for small angular momentum.
K-680
Prove rigorous statements about tails vs memory interaction in near-Kerr: do late-time tails source measurable memory at $\mathcal{I}^+$?
K-685
Prove quantitative stability of the Carter constant for geodesics under small metric perturbations.
K-689
Prove existence and stability of time-periodic near-Kerr solutions (vacuum or with fields) if any.
K-690
Prove robust constraints on nonlinear energy cascades near Kerr (no-turbulence regimes) under small data.
K-693
Prove deterministic stability results for Kerr under stochastic perturbations (noise robustness in PDE sense).
K-694
Prove sharp stability of Kerr under small violations of vacuum Einstein (numerical truncation errors).
K-695
Formalize in a proof assistant: Carter separability and associated conserved quantities for Kerr geodesics.
K-699
Prove that generic near-Kerr perturbations lead to curvature blow-up rates matching those predicted by linear theory.
K-700
Produce a complete, cited dependency graph of Kerr stability research milestones with verified theorem statements.