Prove2Me

EF5 derivative ∂_r Γ^{1}_{00}

Proved
ExactVacuumAtlas.EinsteinMaxwell.EF5.pd_r_G1_00

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

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

EF5 derivative ∂r Γ^{1}{00}

For all real μ, β and x ∈ domU5: the coordinate derivative (pd, coordinate r) of christoffel (gEF5 μ β) (giEF5 μ β) 1 0 0 equals the closed form printed in the statement.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 EF5 Christoffel 符号的坐标导数闭式。

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_EF5_Defs
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.EF5
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.EF5
set_option maxHeartbeats 400000000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
variable (mu beta : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EF5.pd_r_G1_00 {x : Pt 5} (hx : x ∈ domU5) :
    pd 1 (christoffel (gEF5 mu beta) (giEF5 mu beta) 1 0 0) x =
    (2 * mu / x 1 ^ 3 - 4 * beta / x 1 ^ 5) * (mu / x 1 ^ 3 - 2 * beta / x 1 ^ 5) +
    (1 - mu / x 1 ^ 2 + beta / x 1 ^ 4) * (-3 * mu / x 1 ^ 4 + 10 * beta / x 1 ^ 6) := 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/EF5/Ricci.lean#L2829-L2860; SHA-256 f91de831e00ad5d30843158e5baae53dac8ca23c036652f5c758181c627b47f9. 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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