Quasinormal resonances of a massive scalar field in a near-extremal Kerr black hole spacetime

The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived analytically. We show that there exists a critical mass parameter, mu(c), below which increasing the mass mu of the field increases the oscillation frequency R(w) of the resonance. On the other hand, above the critical field mass increasing the mass mu increases the damping rate F(w) of the mode. We confirm our analytical results by numerical computations.