We investigate the quasibound states of charged massive scalar fields in the
Kerr-Newman black hole spacetime by using a new approach recently developed,
which uses the polynomial conditions of the Heun functions. We calculate the
resonant frequencies related to the spectrum of quasibound states, as well as
its corresponding angular and radial wave eigenfunctions. We also analyze the
instability of the system. These results are particularized to the cases of
Schwarzschild and Kerr black holes. Additionally, we compare our analytical
results with the numerical ones known in the literature. Finally, we apply the
obtained results to compute the characteristic times of growth and decay of
bosonic particles around a supermassive black hole situated at the center of
the M87 galaxy.

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