All Problems
110 problems · 92 open · 13 partial · 3 conditional · 1 solved · 1 needs review
This index lists published entries only. Without JavaScript, all published entries remain listed below. Use the chips to filter when scripting is enabled. Unpublished drafts: provisional pipeline.
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-101
Strong Cosmic Censorship threshold for Kerr interiors
K-102
Derive the interior theorem directly from exterior data
K-103
Vacuum curvature blow-up rates on the Kerr Cauchy horizon
K-104
Generic $C^2$- or Lipschitz-inextendibility of near-Kerr MGHDs
K-105
Critical horizon-decay exponent controlling extendibility
K-106
Genericity of lower bounds for linearized-gravity interior instability
K-107
Scattering map to the Cauchy horizon for linearized gravity
K-108
Strong cosmic censorship in rotating $\Lambda>0$ black-hole interiors (conditional on a spectral–interior bridge)
K-109
Near-extremal interior scaling laws
K-110
Global bifurcation-sphere completion for perturbed Kerr-type interiors (vacuum, $\Lambda=0$, Dafermos–Luk class)
K-111
Global interior boundary type: null versus spacelike pieces
K-112
Teukolsky interior asymptotics beyond the current state of the art
K-201
Nonlinear codimension-1 stability of extremal Kerr with horizon hair
K-202
Full linear theory for extremal Kerr (spin 2)
K-203
Nonlinear fate of Aretakis instability
K-204
Uniform estimates in the surface-gravity limit $\kappa \to 0$
K-205
Rigorous near-horizon scattering theory for NHEK
K-206
Extremal interior SCC and Cauchy-horizon regularity
K-207
Extremal tail asymptotics versus conserved charges
K-208
Near-extremal QNM accumulation and branch-cut structure
K-209
Codimension and modulation theory for extremal endstates
K-301
Global smooth Kerr uniqueness without analyticity
K-302
Rigidity for extremal horizons
K-303
Quantitative Kerr characterization via the Mars–Simon tensor
K-304
Near-Kerr rigidity with computable geometric constants
K-305
Kerr characterization from horizon intrinsic data
K-306
Hidden symmetries and approximate Carter-type operators under metric perturbation
K-307
Persistence of normally hyperbolic trapping for dynamical near-Kerr spacetimes
K-308
Rigidity and uniqueness with matter: full Kerr–Newman regime
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-501
Quantitative Mars–Simon tensor gap for near-Kerr stationary vacuum data
K-502
Horizon-data rigidity and effective reconstruction of Kerr parameters
K-503
Uniqueness questions for Carter-type symmetry operators on Kerr
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-508
Stability or obstruction for approximate Killing–Yano tensors near Kerr
K-509
Charge–tail correspondence in the extremal limit
K-608
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-619
Prove uniqueness of stationary black holes with small deviations in asymptotic charges (effective inverse problems).
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-631
Prove a unified framework for gauge choices in nonlinear black-hole stability compatible with $\mathcal{I}^+$ expansions and interior analysis.
K-632
Quantify how much Kerrness can be certified from finite-radius curvature invariants (numerical-relativity certification).
K-642
Prove analogous Cauchy-horizon instability results for coupled gravito-electromagnetic perturbations on Kerr-Newman.
K-644
Prove a full nonlinear characteristic IVP theorem from event-horizon data to the interior boundary in near-Kerr vacuum.
K-645
Quantify the nonlinear backreaction of Price-law tails on Kerr interior geometry (mass inflation vs weak null singularity).
K-649
Formalize in a proof assistant: the exact Kerr separability structure and Carter constant derivation.
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-654
Prove robust boundedness/decay for scalar waves at the Kerr Cauchy horizon in full range and sharp regularity.
K-655
Prove explicit sharp late-time asymptotics for scalar field along the event horizon in Kerr (full range).
K-657
Prove nonlinear evolution of near-horizon conserved quantities in extremal Kerr produces curvature singularity (or not).
K-658
Prove linear stability/instability classification for extremal Kerr-Newman under coupled perturbations.
K-659
Prove sharp resolvent bounds near omega=0 for Kerr linearized Einstein operator, uniform in a/M.
K-661
Determine whether QNM expansions are stable under small nonlinearities (nonlinear resonance theory).
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-666
Prove SCC threshold for Kerr-de Sitter and Kerr-Newman-de Sitter with explicit dependence on spectral gap.
K-667
Prove stability/instability of the Cauchy horizon for Kerr-de Sitter under linearized gravity with sharp norms.
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-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-675
Prove uniqueness/stability of event-horizon generators and their expansion/shear in near-Kerr evolution.
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-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-685
Prove quantitative stability of the Carter constant for geodesics under small metric perturbations.
K-687
Prove a black-hole uniqueness theorem for near Kerr-Newman-de Sitter without analyticity in smooth category.
K-688
Prove a fully rigorous PDE theorem for nonlinear superradiant instability of Kerr in a confining setting (mirror/AdS).
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-692
Prove sharp mapping properties of the Kerr scattering operator in weighted Sobolev spaces matching physical radiation norms.
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-696
Formalize: perturbative uniqueness near Kerr using Mars-Simon tensor estimates (machine-checkable Carleman skeleton).
K-697
Prove that Kerr is uniquely determined among stationary vacua by a finite set of multipole moments with stability.