Prove2Me

KN Ricci component R_{00}

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.ricci_0_0

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

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

KN Ricci component R_{00}

Closed form of ricciOf (gKN) (giKN) at (0, 0) on domReg.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 KN Ricci 分量闭式。

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.ricci_0_0 (x : Pt 4) (hx : x ∈ domReg M a Q) :
    ricciOf (gKN M a Q) (giKN M a Q) 0 0 x = ((-2:ℝ) * M * Q^2) * (x 1) * Ui a (x 1) (x 2) ^ 3 + ((1:ℝ) * a^2 * Q^2) * sin (x 2) ^ 2 * Ui a (x 1) (x 2) ^ 3 + ((1:ℝ) * a^2 * Q^2) * Ui a (x 1) (x 2) ^ 3 + ((1:ℝ) * Q^4) * Ui a (x 1) (x 2) ^ 3 + ((1:ℝ) * Q^2) * (x 1) ^ 2 * Ui a (x 1) (x 2) ^ 3 := 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/Ricci.lean#L25-L39; SHA-256 e817d011c55661ef76e7fc3172a784f05592f4bc47afa248088669235e3c9623. 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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