Prove2Me

Reissner–Nordström (ingoing EF): full Einstein–Maxwell certificate

Proved
ExactVacuumAtlas.EinsteinMaxwell.RN.EF.cert

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

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

Reissner–Nordström (ingoing EF): full Einstein–Maxwell certificate

For all real M, Q: EinsteinMaxwellCertificate (gRN M (Q²)) (giRN M (Q²)) (faradayRN Q) domRN, i.e. the case b = Q² of the RN EF ansatz (see the cert_iff card for the data).

Scope. Every real M, Q; domRN = {r > 0, 0 < θ < π}.

中文摘要 RN（入射 EF，b = Q²）在 domRN 上的完整证书，M、Q 为任意实数。

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
open Real
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.RN
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.RN
set_option maxHeartbeats 4000000
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.RN.EF.cert (M Q : ℝ) :
    EinsteinMaxwellCertificate (gRN M (Q ^ 2)) (giRN M (Q ^ 2)) (faradayRN Q) domRN := 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/RN/EFCert.lean#L187-L190; SHA-256 357f1c6dcc9d4b1de6bc91d8180a4c7e5b75316199ee7ef426a62e658987ab64. 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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