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Generic Christoffel symbols of the Kerr metric equal the closed-form Christoffel symbols

Proved
KerrBL.chrKerr_all

by He Wang · Sep 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

coordinate-geometrygeneral-relativitykerr-metrickerrbl-missionricci-flatness

For all real M,aM,aM,a, every point xxx of the regular domain and all indices i,j,k∈{0,1,2,3}i,j,k\in\{0,1,2,3\}i,j,k∈{0,1,2,3},

Γjki(x)  =  GammaKerrpt M a i j k x,\Gamma^i_{jk}(x)\;=\;\texttt{GammaKerrpt}\ M\ a\ i\ j\ k\ x,Γjki​(x)=GammaKerrpt M a i j k x,

where the left-hand side is the generic coordinate Christoffel symbol christoffel (gKerr M a) (giKerr M a) i j k x of the specification layer, computed from the metric, the candidate inverse and the slice derivatives, and the right-hand side is the generated closed form evaluated at the atoms of xxx.

This is the Christoffel bridge of Layer II. Downstream, the closed forms are differentiated (hdchrKerr_all) and substituted into the Ricci formula (ricci_bridge_Kerr).

Preamble
import Definitions.Def_KerrBL_Kerr_ClosedForms
open KerrBL Filter Topology
Formal statement
theorem KerrBL.chrKerr_all (M a : ℝ) (x : Pt) (hx : RegKerr M a x) :
    ∀ i j k : Fin 4, christoffel (gKerr M a) (giKerr M a) i j k x = GammaKerrpt M a i j k x := by sorry
Source
R. P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237-238, https://doi.org/10.1103/PhysRevLett.11.237; R. H. Boyer and R. W. Lindquist, Maximal analytic extension of the Kerr metric, J. Math. Phys. 8 (1967) 265-281, https://doi.org/10.1063/1.1705193, Sec. 2 (Boyer-Lindquist form of the Kerr line element); metric components transcribed token-for-token from the project certificate EinsteinSolver/certificate/kerr/metric.json (sha256 d729883d95fd7d3cf84d9c971c6725f847155562cc4e88660535b8d0bd0be336); design record LEAN/kerr-formalization/mission/DESIGN.md, node N9 (chrKerr_all)
Human review
  • Endorsed by Shuze Chen · Sep 14, 2026

  • Endorsed by He Wang · Sep 14, 2026

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

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