Symmetries and hidden symmetries for fields outside black holes

TL;DR

This paper reviews methods for establishing decay estimates for various fields outside black holes, highlighting energy techniques and symmetries, with a focus on Maxwell fields in Kerr spacetime.

Contribution

It introduces an approach to proving decay estimates for the Maxwell equation outside a Kerr black hole, emphasizing symmetries and energy methods.

Findings

Energy generation methods are effective for Morawetz estimates.

Symmetries play a crucial role in decay proofs.

An outline for Maxwell field decay outside Kerr is provided.

Abstract

This note surveys how energy generation and strengthening has been used to prove Morawetz estimates for various field equations in Minkowski space, the exterior of the Schwarzschild spacetime, and the exterior of the Kerr spacetime. It briefly outlines an approach to proving a decay estimate for the Maxwell equation outside a Kerr black hole.