Estimates for the Maxwell field near the spatial and null infinity of the Schwarzschild spacetime

TL;DR

This paper develops estimates for the Maxwell field on Schwarzschild spacetime using a specific gauge, aiming to analyze the field's smoothness near spacelike and null infinity.

Contribution

It introduces a gauge-based method to derive estimates for Maxwell fields, enhancing understanding of their behavior at infinity in Schwarzschild spacetime.

Findings

Estimates improve understanding of Maxwell field smoothness at infinity.

Gauge choice facilitates analysis of field behavior near spacelike and null infinity.

Method applicable to a broad class of Maxwell solutions.

Abstract

It is shown how the gauge of the ``regular finite initial value problem at spacelike infinity'' can be used to construct a certain type of estimates for the Maxwell field propagating on a Schwarzschild background. These estimates are constructed with the objective of obtaining information about the smoothness near spacelike and null infinity of a wide class of solutions to the Maxwell equations.