Boundedness and Decay for the Teukolsky System in Kerr-Newman Spacetime II: The Case $|a| \ll M$, $|Q| <M$ in Axial Symmetry

TL;DR

This paper proves boundedness and decay of solutions to the Teukolsky system in slowly rotating, charged Kerr-Newman black holes, using a novel physical-space Morawetz estimate without spherical harmonic decomposition.

Contribution

It introduces a new physical-space Morawetz estimate for the generalized Regge-Wheeler system in Kerr-Newman spacetime, enabling decay results without harmonic analysis.

Findings

Boundedness of solutions established

Polynomial decay rates proven

Applicable to axially symmetric solutions in Kerr-Newman spacetime

Abstract

We establish boundedness and polynomial decay results for the Teukolsky system in the exterior spacetime of very slowly rotating and strongly charged sub-extremal Kerr-Newman black holes, with a focus on axially symmetric solutions. The key step in achieving these results is deriving a physical-space Morawetz estimate for the associated generalized Regge-Wheeler system, without relying on spherical harmonic decomposition.