Prove2Me

Δ > 0 on the exterior

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.domKN_Del_pos

by He Wang · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-vexact-vacuum-atlasgeneral-relativitynewman-penrose

Δ > 0 on the exterior

On domKN M a Q (r > r₊), Δ(r) > 0 for every real M, a, Q (no sub-extremality needed).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 外域上 Δ>0。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_Kerr_InAtoms
open Real
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
open ExactVacuumAtlas.Kerr.In (Ui Wi)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.domKN_Del_pos {M a Q : ℝ} {x : Pt 4} (hx : x ∈ domKN M a Q) :
    0 < Del M a Q (x 1) := by sorry
Source
He Wang, Exact Spacetime Atlas V: From Linearized Einstein–Maxwell Equations to Kerr–Newman Radiation Systems. Local source, no public repository; commit b8cd107a558e153ed41fb4972ac5315499d14778; Atlas/EinsteinMaxwell/KN/Domain.lean#L71-L81; SHA-256 2cba50578710c01bc97b197588f366c9fd153ed1add83d7d7577383f23a9ccce. Registered definitions: mission/PHYSICS_BOUNDARY.md (§K–§M); literature: P. Hintz, arXiv:2609.33661 (v1); Mark–Yang–Zimmerman–Chen, arXiv:1409.5800 (v1).
Human review

  • Endorsed by Shuze Chen · Oct 24, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 24, 2026

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

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