Pointwise decay for the Maxwell field on black hole space-times

TL;DR

This paper proves pointwise decay estimates for solutions to the Maxwell equations on certain nonstationary black hole backgrounds, assuming energy bounds and local decay, advancing understanding of electromagnetic fields in curved spacetime.

Contribution

It establishes peeling decay estimates for Maxwell fields on nonstationary black hole spacetimes under minimal energy assumptions, extending previous stationary results.

Findings

Peeling estimates for Maxwell tensor components

Decay rates depend on energy bounds and local decay

Applicable to nonstationary asymptotically flat backgrounds

Abstract

In this article we study the pointwise decay properties of solutions to the Maxwell system on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time, we establish peeling estimates for all the components of the Maxwell tensor.