About

Kerr Problems is primarily a mathematical relativity database: open questions stated in PDE, geometry, and spectral language around Kerr and closely related rotating black-hole models. Some entries are physics-facing (motivated by observation or astrophysical language) while remaining mathematical statements; others are pure-math in motivation. The orthogonal relevance tag records that distinction without mixing it into cluster navigation.

The word “Kerr” is used in several senses on this site: the exact vacuum Kerr solution; dynamical perturbations near it in vacuum; charged (Kerr–Newman) extensions; Λ ≠ 0 backgrounds (Kerr–de Sitter, Kerr–AdS); and near-horizon extremal limits (NHEK). Exact Kerr, near-Kerr vacuum, Kerr–Newman, Kerr–dS, Kerr–AdS, and NHEK require separate tagging because asymptotics, matter coupling, and boundary problems are not interchangeable.

Clusters are coarse research themes (five total). Orthogonal tags carry the nuance: what geometry, what equations, what regime, and how formalization-friendly the statement might be. A problem in “Exterior stability” can still be Kerr–AdS or matter-coupled; read the tags and any caution_note on the problem page.

The formal verification track explains heuristic suitability for proof assistants and lists curated entries K-501–K-510 plus other high/medium FV problems.

Status labels

open No theorem in the stated form is currently known (on this site’s reading).
partial Important special cases, reductions, or adjacent results exist.
conditional Progress assumes a identified missing input or restricted hypothesis class.
solved A complete theorem in the stated form is known.

Difficulty ratings (1–5) are heuristic, not permanent verdicts.

Orthogonal metadata tags

Documented in data/schema.md and enforced by npm run validate.

Orthogonal tags (quick reference)

Theorem status: Open / partial / conditional / solved / needs review — solution progress, orthogonal to problem type.
Problem type: Classical frontier vs quantitative sharpening vs formalization target, etc.
Research state: Literature-solved vs open-in-literature vs high-value unformalized / synthesized targets.
Family: Exact Kerr vs near-Kerr vacuum vs Kerr–Newman, Λ ≠ 0, NHEK, or broader rotating families.
Asymptotics: Asymptotically flat, de Sitter, AdS, or mixed settings (not interchangeable).
Coupling: Vacuum Einstein vs matter-coupled (e.g. Einstein–Maxwell).
Equation level: Scalar/Maxwell/linearized gravity/full Einstein, reductions, spectral operators, inverse problems.
Regime: Stationary vs dynamical; linear vs nonlinear; exterior/interior; extremal/near-extremal.
Relevance: Pure math vs mixed vs physics-facing motivation.
FV suitability: Heuristic formal-verification friendliness (high / medium / low) with a short reason on each problem.

Allowed values (summary)

family: exact-kerr, near-kerr-vacuum, kerr-newman, kerr-de-sitter, kerr-ads, nhek, related-rotating-black-hole
asymptotics: asymptotically-flat, de-sitter, anti-de-sitter, mixed
coupling: vacuum, matter-coupled
equation_level: null-geodesics, scalar-wave, maxwell, linearized-gravity, full-einstein, einstein-maxwell, stationary-reduction, spectral-operator, inverse-problem
regime: stationary, linear, nonlinear, exterior, interior, extremal, near-extremal
relevance: pure-math, mixed, physics-facing
fv_suitability: high, medium, low (plus required fv_reason string)
dependencies / related: arrays of problem IDs; progress_summary must stay conservative (no fabricated theorems)

What counts as a Kerr problem here?

Any rigorously stated question where the Kerr geometry, its standard perturbations, or a clearly labeled Kerr-related family (charged, Λ ≠ 0, near-horizon limit, rotating black-hole cousins) is essential to the mathematical formulation. If the title says “Kerr” but the content is broader, look for related_families_note and caution_note on the problem page.

Which problems are pure mathematics, and which are physics-facing?

Use the relevance badge. Pure-math entries emphasize geometric / analytic / foundational questions without observational framing. Physics-facing entries may use language from astrophysics or detectors but should still be mathematical statements. Mixed is intentional overlap. Physics-facing wording on a pure-math tag should carry a caution_note when the mismatch could confuse readers.

Which problems are promising for formal verification?

See fv_suitability and fv_reason on each problem, and the dedicated Formal verification page for criteria and curated lists (including K-501–K-510). High suitability usually means stationary structure, ODE/separable models, or finite- dimensional rigidity — not full nonlinear global Einstein evolution.

Contributing

Problems live as YAML in the GitHub repository. Pull requests should preserve schema validity (npm run validate). See CONTRIBUTING.md. For accuracy concerns, open an issue or email admin@kerrproblems.com.