The Kerr-Newman spacetime is the most general explicit black hole solution, and represents a stationary rotating charged black hole. Its stability to gravitational and electromagnetic perturbations has eluded a proof since the 80s in the black hole perturbation community. As put by Chandrasekhar, "the methods that have proved to be so successful in treating the gravitational perturbations of the Kerr spacetime do not seem to be applicable for treating the coupled electromagnetic-gravitational perturbations of the Kerr-Newman spacetime". He adds, "the principle obstacle is in finding separated equations".
Following the road map that mathematicians have taken in interpreting in physical space the known mode analysis, we will present a way to overcome "the apparent indissolubility of the coupling between the spin-1 and spin-2 fields in the perturbed spacetime". We will explain how the decomposition in modes, done to simplify the analysis of the equations, makes them unsolvable when electromagnetic and gravitational radiations interact. We instead generalize the Chandrasekhar transformation to Kerr-Newman in physical space and use it to obtain a quantitative proof of stability.