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The quasi-bound states of charged massive scalar fields in the near-extremalcharged Reissner-Nordstr\"om black-hole spacetime are studied {\itanalytically}. These discrete resonant modes of the composed black-hole-fieldsystem are characterized by the physically motivated boundary condition ofingoing waves at the black-hole horizon and exponentially decaying (bounded)radial eigenfunctions at spatial infinity. Solving the Klein-Gordon waveequation for the linearized scalar fields in the black-hole spacetime, wederive a remarkably compact analytical formula for the complex frequencyspectrum which characterizes the quasi-bound state resonances of the composedReissner-Nordstr\"om-black-hole-charged-massive-scalar-field system.

Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner-Nordstr\"om black-hole spacetime