The generic Ricci tensor of the Kerr metric equals the explicit closed-form expression
ProvedKerrBL.ricci_bridge_Kerrcoordinate-geometrygeneral-relativitykerr-metrickerrbl-missionricci-flatness
For all real , every point of the regular domain and all indices ,
where ricciOf (gKerr M a) (giKerr M a) b d x is the generic derivative-based coordinate Ricci tensor of the specification layer, and RicciKerr is the explicit expression of KerrBL_Kerr_ClosedForms.
This is the bridge from the specification to the explicit expressions whose vanishing Layer III proves. The explicit Ricci expression is never assumed: this theorem derives it from the generic definitions together with the Christoffel bridge and the Christoffel-derivative certification.
Preamble
import Definitions.Def_KerrBL_Kerr_ClosedForms open KerrBL Filter Topology
Formal statement
theorem KerrBL.ricci_bridge_Kerr (M a : ℝ) (x : Pt) (hx : RegKerr M a x) (b d : Fin 4) :
ricciOf (gKerr M a) (giKerr M a) b d x = RicciKerr M a b d (x 1) (Real.sin (x 2)) (Real.cos (x 2)) (Sig a (x 1) (Real.cos (x 2))) (Del M a (x 1)) := by sorrySource
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 N12 (ricci_bridge_Kerr)
Human review
Confirmed by the mission captain (proposal self-audit).