Prove2Me

IV's Maxwell stress in a null frame

Proved
ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData.emStressF_eq

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

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

IV's Maxwell stress in a null frame

For a null frame: S(e_A, e_B) = (F η Fᵀ){AB} − ¼ η{AB} Σ_{CD} F_{CD}(η F η)_{CD}, F the matrix of frame components (η⁻¹ = η).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 零标架中 IV 的 Maxwell 应力。

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_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_EinsteinMaxwell_NP_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_NP_CCalc
import Definitions.Def_Atlas_EinsteinMaxwell_NP_FrameConn
import Definitions.Def_Atlas_EinsteinMaxwell_NP_FrameNull
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNFrame
import Definitions.Def_Atlas_EinsteinMaxwell_NP_Riemann
import Definitions.Def_Atlas_Kerr_InAtoms
import Definitions.Def_Atlas_Transport_Connection
import Definitions.Def_Atlas_Transport_MatrixCalc
open scoped ContDiff Matrix
open Complex
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.NP
open ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData
variable {g gi : Metric 4} {E Θ : Fin 4 → Fin 4 → Pt 4 → ℂ} {U : Set (Pt 4)}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData.emStressF_eq (hN : NullFrameData g gi E Θ U) {x : Pt 4} (hx : x ∈ U) (F : TwoForm 4) (A B : Fin 4) :
    ccontr (emStress g gi F) x (fvec E A x) (fvec E B x)
      = (FfrM F E x * etaNull * (FfrM F E x)ᵀ) A B
        - etaNull A B * (∑ C, ∑ D, FfrM F E x C D * (etaNull * FfrM F E x * etaNull) C D) / 4 := 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/NP/FrameNull.lean#L460-L488; SHA-256 89b93964d08a58f81f17ec29d939043c67b8a5c7a9a375bb5c15b99bf70dff0a. 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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