Slowly decaying resonances of charged massive scalar fields in the Reissner–Nordström black-hole spacetime

We determine the characteristic timescales associated with the linearized relaxation dynamics of the composed Reissner–Nordström-black-hole-charged-massive-scalar-field system. To that end, the quasinormal resonant frequencies {ωn(μ,q,M,Q)}n=0n=∞ which characterize the dynamics of a charged scalar field of mass μ and charge coupling constant q in the charged Reissner–Nordström black-hole spacetime of mass M and electric charge Q are determined analytically   in the eikonal regime 1≪Mμ