Quasinormal modes of massive vector fields on the Kerr spacetime

We study the spectrum of quasinormal mode frequencies for a Proca field on a rotating black hole spacetime. First, we review how the introduction of field mass modifies the spectrum in the scalar-field case, leading to evanescent modes and to quasiresonance. Next, we examine the three physical polarizations of the Proca field and their relation to the electromagnetic field modes in the massless limit. Exploiting a separation of variables, we obtain a five-term recurrence relation from an appropriate ansatz for the radial function. Gaussian elimination and the modified Lentz algorithm are applied, and the quasinormal frequencies are computed from the roots of a continued fraction. We validate our method by calculating quasibound state frequencies, which are complementary to quasinormal modes, and which can be calculated using the same method. We present a selection of results for the low-lying overtones of all three polarizations, across a range of black hole spins and field masses.