Prove2Me

KN at Q = 0 gives the Kerr BL vacuum certificate on the exterior

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.vacuum_exterior_of_cert_Q0

by He Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity

KN at Q = 0 gives the Kerr BL vacuum certificate on the exterior

For M > 0 and real a: VacuumCertificate (KerrBL.gKerr M a) (KerrBL.giKerr M a) (domKN M a 0), where gKerr, giKerr are the published TASK-001A Kerr Boyer–Lindquist definitions and VacuumCertificate is the release-I definition (open, nonempty, symmetric, true inverse, C^∞, Lorentzian, ricciOf = 0). Obtained from the KN certificate at Q = 0 (F = 0) by componentwise equality of the data on the common domain.

Scope. Parameter substitution Q = 0 on a common open domain; nothing for Q ≠ 0 is inferred from Kerr; independent of Verified.Kerr.

中文摘要 Q = 0 特化：由 KN 证书导出 Kerr BL 真空证书（外域，M>0）；参数代入，不是极限。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_EinsteinMaxwell_RNStd_Defs
import Definitions.Def_Atlas_Kerr_Frame
import Definitions.Def_Atlas_Kerr_InAtoms
import Definitions.Def_KerrBL_CoordGeometry
import Definitions.Def_KerrBL_Kerr_Metric
open Real
open scoped ContDiff
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.vacuum_exterior_of_cert_Q0 (M a : ℝ) (hM : 0 < M) :
    VacuumCertificate (KerrBL.gKerr M a) (KerrBL.giKerr M a) (domKN M a 0) := by sorry
Source
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/EinsteinMaxwell/KN/Special.lean#L1618-L1623; SHA-256 8ec8234538cef3eac7f462a57128cdaa80597af52a2efef1190c8df8425ba5a3. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review

  • Endorsed by Shuze Chen · Oct 21, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 21, 2026

    Confirmed by the mission captain (proposal self-audit).

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