Prove2Me

RN mass/charge tangents solve the linearised equations

Proved
ExactVacuumAtlas.Variation.RN.param_tangent

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

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

RN mass/charge tangents solve the linearised equations

For all real M, Q, m, q and x ∈ domRN, with background (gRN M (Q²), giRN M (Q²), faradayRN Q) and the explicit tangent h = tanRN Q m q (only h_vv = 2m/r − 2Qq/r²), f = tanFRN q (f_vr = −q/r², f_rv = q/r²): LE_ab = 0 for all a, b, LJ^b = 0 for all b, LH_abc = 0 for all a, b, c.

Scope. The tangent is the true ε-derivative of the RN family (M + εm, Q + εq) (familyData_param, isTangent_param); zero follows from the off-shell bridge applied to a family of certificates. First-order statement only.

中文摘要 RN 质量/电荷参数切向（显式 h_vv=2m/r−2Qq/r²，f_rv=q/r²）满足线性化方程（LE=LJ=LH=0）。

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.param_tangent (M Q m q : ℝ) {x : Pt 4} (hx : x ∈ domRN) :
    (∀ a b, linEinstein (gRN M (Q ^ 2)) (giRN M (Q ^ 2)) (faradayRN Q) (tanRN Q m q) (tanFRN q) a b x = 0) ∧
    (∀ b, linMaxwell (gRN M (Q ^ 2)) (giRN M (Q ^ 2)) (faradayRN Q) (tanRN Q m q) (tanFRN q) b x = 0) ∧
    (∀ a b c, linFaraday (tanFRN q) a b c 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/Variation/RN.lean#L133-L152; 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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