Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric

Understand

We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable.

• As an illustration of the method we investigate massive vector (Proca) perturbations in the Kerr metric, which do not appear to be separable in the standard Teukolsky formalism.
• Working in a perturbative scheme, we discuss two important effects induced by rotation: a Zeeman-like shift of nonaxisymmetric quasinormal modes and bound states with different azimuthal number m, and the coupling between axial and polar modes with different multipolar index l.
• We explicitly compute the perturbation equations up to second order in rotation, but in principle the method can be extended to any order.