Prove2Me

VI-01 fixed static EF ansatz in five dimensions

Definition
Atlas_EinsteinMaxwell_EF5_Defs

by He Wang · Oct 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity

VI-01 fixed static EF ansatz in five dimensions

domU5 = {0 < r, 0 < u < 1}; gEF5 μ β = −f dv² + 2 dv dr + r²[du²/(4u(1−u)) + u dφ² + (1−u) dψ²], f = 1 − μ/r² + β/r⁴; explicit inverse giEF5; emPot5 Q = −Q/(2r²) dv; faraday5 Q (F_10 = Q/r³ = −F_01). All real μ, β, Q.

中文摘要 VI-01 五维固定静态 EF 拟设及其定义域。

Registry: PHYSICS_BOUNDARY §N (VI-01) N4.

Definition code
-- Generated by scripts/release06/gen_platform_tree.py (RELEASE06; copy of release05, header only) by skeleton subtraction from Atlas/EinsteinMaxwell/EF5/Defs.lean
-- definition bundle: kept ExactVacuumAtlas.EinsteinMaxwell.EF5.domU5, ExactVacuumAtlas.EinsteinMaxwell.EF5.emPot5, ExactVacuumAtlas.EinsteinMaxwell.EF5.faraday5, ExactVacuumAtlas.EinsteinMaxwell.EF5.gEF5, ExactVacuumAtlas.EinsteinMaxwell.EF5.giEF5
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_D_Basic
set_option maxHeartbeats 4000000
set_option linter.unusedVariables false

open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D

namespace ExactVacuumAtlas.EinsteinMaxwell.EF5

def domU5 : Set (Pt 5) := {x | 0 < x 1 ∧ 0 < x 2 ∧ x 2 < 1}

noncomputable def gEF5 (mu beta : ℝ) : Metric 5
  | 0, 0 => fun x => -(1 - mu / x 1 ^ 2 + beta / x 1 ^ 4)
  | 0, 1 => fun _ => 1
  | 1, 0 => fun _ => 1
  | 2, 2 => fun x => x 1 ^ 2 / (4 * x 2 * (1 - x 2))
  | 3, 3 => fun x => x 1 ^ 2 * x 2
  | 4, 4 => fun x => x 1 ^ 2 * (1 - x 2)
  | _, _ => fun _ => 0

noncomputable def giEF5 (mu beta : ℝ) : Metric 5
  | 0, 1 => fun _ => 1
  | 1, 0 => fun _ => 1
  | 1, 1 => fun x => 1 - mu / x 1 ^ 2 + beta / x 1 ^ 4
  | 2, 2 => fun x => 4 * x 2 * (1 - x 2) / x 1 ^ 2
  | 3, 3 => fun x => 1 / (x 1 ^ 2 * x 2)
  | 4, 4 => fun x => 1 / (x 1 ^ 2 * (1 - x 2))
  | _, _ => fun _ => 0

noncomputable def emPot5 (Q : ℝ) : CoVec 5
  | 0 => fun x => -Q / (2 * x 1 ^ 2)
  | _ => fun _ => 0

noncomputable def faraday5 (Q : ℝ) : TwoForm 5
  | 1, 0 => fun x => Q / x 1 ^ 3
  | 0, 1 => fun x => -Q / x 1 ^ 3
  | _, _ => fun _ => 0

/-! ## Smoothness -/

end ExactVacuumAtlas.EinsteinMaxwell.EF5
Source
He Wang, Exact Spacetime Atlas VI: Five-Dimensional Einstein–Maxwell Certificates and Equal-Spin Radial Reduction. Local source, no public repository; commit 4a4048a; Atlas/EinsteinMaxwell/EF5/Defs.lean; SHA-256 f231f4a9949f874f4e55d1d1a5d115dc989dd2dea043b61580e11ec6dcfcc0ca. Registered definitions: mission/PHYSICS_BOUNDARY.md (§N–§O); literature: R. C. Myers, M. J. Perry, Ann. Phys. 172 (1986) 304; F. R. Tangherlini, Nuovo Cimento 27 (1963) 636.
Human review

  • Endorsed by Shuze Chen · Oct 29, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 29, 2026

    Confirmed by the mission captain (proposal self-audit).

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