The superradiant stability of a Kerr–Newman black hole and charged massive scalar perturbation is investigated. We treat the black hole as a background geometry and study the equation of motion of the scalar perturbation. From the radial equation of motion, we derive the effective potential experienced by the scalar perturbation. By a careful analysis of this effective potential, it is found that when the inner and outer horizons of Kerr–Newman black hole satisfy $$\frac{r_-}{r_+}\leqslant \frac{1}{3}$$
r
-
r
+
⩽
1
3
and the charge-to-mass ratios of scalar perturbation and black hole satisfy $$ \frac{q}{\mu }\frac{Q}{ M}>1 $$
q
μ
Q
M
>
1
, the Kerr–Newman black hole and scalar perturbation system is superradiantly stable.
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