Rigorous near-horizon scattering theory for NHEK

open Extremal / Near-Extremal

Statement

Construct a mathematically precise scattering theory for the near-horizon extremal Kerr limit and prove convergence from rescaled near-extremal Kerr dynamics.

Mathematical prerequisites

Geometric blow-up limits; near-horizon analysis; scattering on non-asymptotically-flat geometries; matched expansions.

Why it matters

The near-horizon extremal geometry is the natural local model controlling many extremal phenomena.

Completion criteria

A complete answer must prove operator and solution convergence under rescaling and define a genuine scattering theory in the limit geometry.

Implications if solved

Would isolate the intrinsic throat dynamics responsible for extremal instabilities.

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