EF5 derivative ∂_v Γ^{0}_{22}
ProvedExactVacuumAtlas.EinsteinMaxwell.EF5.pd_v_G0_22einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity
EF5 derivative ∂v Γ^{0}{22}
For all real μ, β and x ∈ domU5: the coordinate derivative (pd, coordinate v) of christoffel (gEF5 μ β) (giEF5 μ β) 0 2 2 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_v_G0_22 {x : Pt 5} (hx : x ∈ domU5) :
pd 0 (christoffel (gEF5 mu beta) (giEF5 mu beta) 0 2 2) x = 0 := by sorrySource
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#L980-L993; 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
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.