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

Understand

We prove boundedness and polynomial decay statements for solutions of the Teukolsky system for electromagnetic-gravitational perturbations of a Kerr-Newman exterior background, with parameters satisfying $|a|, |Q| \ll M$.

• The identification and analysis of the Teukolsky system in Kerr-Newman has long been problematic due to the long-standing problem of coupling and failure of separability of the equations.
• Here, we analyze a system satisfied by novel gauge-invariant quantities representing gravitational and electromagnetic radiations for coupled perturbations of a Kerr-Newman black hole.
• The bounds are obtained by making use of a generalization of the Chandrasekhar transformation into a system of coupled generalized Regge-Wheeler equations derived in previous work.