Photon-region and trapping stability in dynamical near-Kerr spacetimes

open Rigidity / Uniqueness

Statement

Show that the normally hyperbolic trapped set of Kerr persists, in a quantitatively useful sense, under dynamical perturbations compatible with nonlinear stability.

Mathematical prerequisites

Dynamical systems near trapped sets; semiclassical propagation; microlocal resolvent estimates; time-dependent geometry.

Why it matters

Trapping is one of the main analytic obstacles in every decay estimate on Kerr.

Completion criteria

A complete answer must prove persistence of the trapped structure and derive Morawetz or resolvent consequences from it.

Implications if solved

Would provide a geometric backbone for robust decay theory on dynamical near-Kerr backgrounds.

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