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

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.

23 pages. A Mathematica notebook containing all the computations is attached as ancillary file. All comments are welcome!