  We investigate the instability of charged massive scalar fields in
Kerr-Newman spacetime. Due to the super-radiant effect of the background
geometry, the bound state of the scalar field is unstable, and its amplitude
grows in time. By solving the Klein-Gordon equation of the scalar field as an
eigenvalue problem, we numerically obtain the growth rate of the amplitude of
the scalar field. Although the dependence of the scalar field mass and the
scalar field charge on this growth rate agrees with the result of the analytic
approximation, the maximum value of the growth rate is three times larger than
that of the analytic approximation. We also discuss the effect of the electric
charge on the instability of the scalar field.
