Prove2Me

KN at a = 0 gives the Reissner–Nordström certificate in standard coordinates

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.certStdRN

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

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

KN at a = 0 gives the Reissner–Nordström certificate in standard coordinates

For M > 0 and real Q: EinsteinMaxwellCertificate (gStdRN M Q) (giStdRN M Q) (faradayStdRN Q) (domStdRN M Q), with coordinates (t, r, θ, φ), gStdRN = diag(−f, 1/f, r², r² sin²θ), f = 1 − 2M/r + Q²/r², giStdRN = diag(−1/f, f, r⁻², (r² sin²θ)⁻¹), F_rt = Q/r² = −F_tr, domStdRN = {M + √(M² − Q²) < r, 0 < θ < π}. Obtained by specialising the KN certificate to a = 0.

Scope. Parameter substitution a = 0 (equality of data on domKN M 0 Q = domStdRN M Q). Not the ingoing-EF chart of milestone 1; no EF ↔ standard coordinate relation is claimed.

中文摘要 a = 0 特化：标准坐标 RN 的完整证书；这不是 IV-01 的 EF 坐标，也不声称 EF↔标准坐标映射。

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_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_EinsteinMaxwell_RNStd_Defs
import Definitions.Def_Atlas_Kerr_Frame
import Definitions.Def_Atlas_Kerr_InAtoms
import Definitions.Def_KerrBL_CoordGeometry
import Definitions.Def_KerrBL_Kerr_Metric
open Real
open scoped ContDiff
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.certStdRN (M Q : ℝ) (hM : 0 < M) :
    EinsteinMaxwellCertificate (RNStd.gStdRN M Q) (RNStd.giStdRN M Q) (RNStd.faradayStdRN Q)
      (RNStd.domStdRN M Q) := 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/Special.lean#L1633-L1641; SHA-256 8ec8234538cef3eac7f462a57128cdaa80597af52a2efef1190c8df8425ba5a3. 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).

View graph