Massless Maxwell fields on sub-extremal Kerr-Newman exteriors

TL;DR

This paper proves boundedness, decay, and scattering results for massless Maxwell fields on sub-extremal Kerr-Newman black hole exteriors, covering various rotation and charge regimes.

Contribution

It establishes comprehensive energy estimates and decay properties for Maxwell fields on Kerr-Newman backgrounds across multiple parameter regimes, including full sub-extremal range.

Findings

Proved non-degenerate boundedness and decay of Maxwell fields.

Established Morawetz and local energy decay estimates.

Achieved scattering results for stationary-subtracted Maxwell fields.

Abstract

We study the massless Maxwell system on fixed sub--extremal Kerr-Newman exteriors. In the weak Kerr--Newman regimes with $0<|a|\le c_a M$, $0<|Q|\le c_Q M$, and $c_a,c_Q \in (0,1) $, we prove non--degenerate boundedness, Morawetz / integrated local energy decay, the outgoing $r^p$ hierarchy, radiation fields, polynomial decay, and two--sided scattering for the stationary-subtracted Maxwell field. In the axisymmetric relative slow--rotation regime $0<|a|\le \varepsilon_{\mathrm{KN}}|Q|<M$ with $\varepsilon_{\mathrm{KN}} \in (0,1)$, the same conclusions hold on the axisymmetric sector, with no perturbative restriction on $|Q|/M$ beyond sub--extremality. For the full sub-extremal range $a^2+Q^2<M^2$, by adding one order--zero radiative local--energy estimate for this master system, we could obtain similar results as the weak regimes. This separates the unconditional weak theory from the conditional full--range theory within one reconstruction/scattering framework.