Exact algebraic separation of the gravitoelectromagnetic perturbations of Kerr-Newman-(anti-)de Sitter black holes

Abstract

We obtain an explicit separation of the coupled gravitational and electromagnetic radiative equations on nonextremal Kerr--Newman--(anti-)de Sitter black holes with nonzero charge and rotation. The construction uses a matrix with constant determinant, chosen independently of the frequency and azimuthal number, and treats the positive- and negative-spin sectors within the same formulation. We establish that this transformation is smooth and invertible throughout the open AdS exterior and between the event and cosmological horizons in dS. The resulting radial and angular systems are valid at arbitrary complex frequencies. We also express regularity of the radiative Newman--Penrose variables at the rotation axes and future horizons as conditions on the separated solutions. In the asymptotically flat limit, the transformation is related to Hintz's matrix integrating factor by the allowed frame freedom. These results provide a basis for studying quasinormal modes and black-hole stability in Kerr--Newman--(anti-)de Sitter spacetimes, as well as exploring holographic applications to strongly coupled systems.