Prove2Me

Value LE_θθ = 1/r² of the RN b-direction

Proved
ExactVacuumAtlas.Variation.RN.nonzero_theta

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

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

Value LE_θθ = 1/r² of the RN b-direction

For all real M, Q and x ∈ domRN: LE_θθ(gRN M (Q²), giRN M (Q²), faradayRN Q; tanB, 0)(x) = 1/r² (r = x¹).

Scope. Same operator LE as the goal; no test-specific operator.

中文摘要 RN b 方向的 LE_θθ 精确值 1/r²。

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_RN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_RN_Frame
import Definitions.Def_Atlas_EinsteinMaxwell_Variation_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_Variation_RN
import Definitions.Def_Atlas_Transport_MatrixCalc
open Real
open scoped ContDiff
open ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.RN
Formal statement
theorem ExactVacuumAtlas.Variation.RN.nonzero_theta (M Q : ℝ) {x : Pt 4} (hx : x ∈ domRN) :
    linEinstein (gRN M (Q ^ 2)) (giRN M (Q ^ 2)) (faradayRN Q) tanB 0 2 2 x = 1 / x 1 ^ 2 := 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/Variation/RN.lean#L156-L170; SHA-256 7513cd6c91a5e550bb62e1cac2f2c8a8c17fa469087ba3c27bf9c1eab933f66f. 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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