Prove2Me

KN Einstein residual E_{00} = 0

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.einstein_0_0

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

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

KN Einstein residual E_{00} = 0

einsteinMaxwell (gKN) (giKN) (faradayKN) 0 0 = 0 on domReg.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 KN Einstein 残差分量为零。

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 scoped ContDiff
open ExactVacuumAtlas.Kerr.In (Ui Wi)
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
set_option maxHeartbeats 8000000
set_option maxRecDepth 100000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
variable (M a Q : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.einstein_0_0 (x : Pt 4) (hx : x ∈ domReg M a Q) :
    einsteinMaxwell (gKN M a Q) (giKN M a Q) (faradayKN a Q) 0 0 x = 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/Einstein.lean#L40-L44; SHA-256 63a254f176601e5da05dba1f10f10a220b1f1056f8d0aa253e2664d1d7518a5e. 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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