K-007

Einstein–Maxwell stability near Kerr

partial Exterior Stability

Statement

Prove asymptotic stability for coupled gravitational and electromagnetic perturbations near a rotating black-hole endstate.

Mathematical prerequisites

Coupled hyperbolic systems; gravito-electromagnetic gauge fixing; Teukolsky-type equations with coupling; conserved fluxes for charge and angular momentum.

Why it matters

Realistic black-hole models often involve coupled fields, and the Einstein–Maxwell system is the next natural extension of the vacuum problem.

Completion criteria

A complete answer must identify the final stationary family, derive quantitative decay for the coupled fields, and prove orbital stability in a precise topology.

Implications if solved

Would open a path toward the full Kerr–Newman stability program.

Last updated: 2026-04-05 · Edit on GitHub →