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In Einstein-Maxwell theory, according to classic uniqueness theorems, themost general stationary black-hole solution is the axisymmetric Kerr-Newmanmetric, which is defined by three parameters: mass, spin and electric charge.The radial and angular dependence of gravitational and electromagneticperturbations in the Kerr-Newman geometry do not seem to be separable. In thispaper we circumvent this problem by studying scalar, electromagnetic andgravitational perturbations of Kerr-Newman black holes in the slow-rotationlimit. We extend (and provide details of) the analysis presented in a recentLetter [arXiv:1304.1160]. Working at linear order in the spin, we present thefirst detailed derivation of the axial and polar perturbation equations in thegravito-electromagnetic case, and we compute the corresponding quasinormalmodes for any value of the electric charge. Our study is the firstself-consistent stability analysis of the Kerr-Newman metric, and in principleit can be extended to any order in the small rotation parameter. We findnumerical evidence that the axial and polar sectors are isospectral at firstorder in the spin, and speculate on the possible implications of this result.

Scalar, Electromagnetic and Gravitational Perturbations of Kerr-Newman Black Holes in the Slow-Rotation Limit