Peeling of Dirac and Maxwell fields on a Schwarzschild background

TL;DR

This paper investigates the decay and regularity properties of Dirac and Maxwell fields on a Schwarzschild black hole background, extending techniques from Minkowski space and demonstrating similar behavior across null infinity.

Contribution

It adapts the peeling approach to Dirac and Maxwell fields on Schwarzschild spacetime using conformal compactification and vector field methods, establishing optimal initial data spaces.

Findings

Decay and regularity assumptions in Minkowski and Schwarzschild are equivalent across null infinity.

Results apply to a class of asymptotically simple spacetimes.

Method provides a framework for analyzing field behavior at null infinity.

Abstract

We study the peeling of Dirac and Maxwell fields on a Schwarzschild background following the approach developed by the authors in Mason-Nicolas 2009 for the wave equation. The method combines a conformal compactification with vector field techniques in order to work out the optimal space of initial data for a given transverse regularity of the rescaled field across null infinity. The results show that analogous decay and regularity assumptions in Minkowski and in Schwarzschild produce the same regularity across null infinity. The results are valid also for the classes of asymptotically simple spacetimes constructed by Corvino-Schoen / Chrusciel-Delay.