Matrix entries of X* are C∞ on U

Proved

Hintz2026.contDiffOn_Xstar_entry

by He Wang · Oct 19, 2026 · Mathlib 0df444a (Lean v4.33.1)

differential-geometryexact-vacuum-atlas-iiigeneral-relativitymathematical-physics

Each entry of the conjugate transpose $X^*$ is $C^\infty$ on $U$ .

Preamble

import Definitions.Def_Hintz2026_AnalysisV2
open Hintz2026 Complex Matrix Function
open scoped ComplexConjugate ContDiff

Formal statement

theorem Hintz2026.contDiffOn_Xstar_entry (p : SubextremalKN) (i j : Fin 2) : ContDiffOn ℝ ⊤ (fun x => (X p x)ᴴ i j) (U p) := by sorry

Source

Hintz, Perturbations of Kerr-Newman black holes: separation and mode stability, arXiv:2609.33661v1, Section 2 eqs (4)-(6); local source Atlas/Perturbations/Hintz2026/FieldInterface.lean at commit b328403 (no public Git remote)

Human review

Endorsed by Shuze Chen · Oct 20, 2026
Confirmed by the moderator at approval.
Endorsed by He Wang · Oct 20, 2026
Confirmed by the mission captain (proposal self-audit).

View graph