Nonlinear wave equations on Kerr black hole spacetimes with slowly rotating angular momentum

What the research examines

Proves global existence and asymptotic stability of solutions to quasilinear wave equations satisfying the null condition on sub-extremal Kerr spacetimes, establishing uniform vector-field energy estimates across trapped photon spheres.

Why it may matter

Provides indispensable mathematical scaffolding toward proving the full non-linear stability of the Kerr metric in General Relativity.

What to examine carefully

Assumes slow rotation parameter |a| << M, leaving open the rapidly spinning near-extremal Kerr black hole regime.

Try a small, reproducible follow-up

Formulate the Teukolsky master equation in Boyer-Lindquist coordinates and compute quasi-normal mode frequencies using Leaver's continued fraction method.

Questions to investigate

1. How was the trapping degeneracy on the photon sphere resolved without losing derivative regularity?
2. What Morawetz integrated energy decay estimates were established outside the event horizon?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources