Prove2Me

Equal-spin frame diagonalises the metric

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.esFrame_spec

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

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

Equal-spin frame diagonalises the metric

For x with x 2 ≠ 0 and 1 − x 2 ≠ 0: (esFrame W x)ᵀ · esMetric · esFrame W x equals the diagonal matrix printed in the statement.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 等自旋显式标架将度规对角化。

Preamble
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
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Defs
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.ES5
set_option maxHeartbeats 8000000
variable (B D A H W : ℝ → ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.esFrame_spec (x : Pt 5) (hu : x 2 ≠ 0) (hv : 1 - x 2 ≠ 0) :
    (esFrame W x).transpose * metricMatrix (esMetric B D A H W) x * esFrame W x =
      Matrix.diagonal ![-B (x 1), D (x 1), A (x 1) / (4 * x 2 * (1 - x 2)), H (x 1),
        A (x 1) * x 2 * (1 - x 2)] := by sorry
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/ES5/Defs.lean#L134-L141; SHA-256 bb9c71fdcb4c409e9bfd1766a9ca9bb3118fe200aee50524ee3c961baaa00f90. 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).

View graph