Linear Stability of the Non-Extreme Kerr Black Hole

TL;DR

This paper proves that solutions to the Teukolsky equation for Kerr black holes decay over time, demonstrating stability for non-extreme Kerr black holes under certain initial conditions.

Contribution

It provides a rigorous proof of decay for all azimuthal modes of the Teukolsky equation in non-extreme Kerr black holes, establishing their linear stability.

Findings

Solutions decay pointwise in time

Decay holds for all azimuthal modes

Initial data with compact support outside the horizon

Abstract

It is proven that for smooth initial data with compact support outside the event horizon, the solution of every azimuthal mode of the Teukolsky equation for general spin decays pointwise in time.