  The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by
performing numerical simulations within the full Einstein-Maxwell theory. We
take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$
and charge $Q$. Evolutions are performed to scan this parameter space within
the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an
extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$)
ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small
bar-mode perturbation, up to a time of order $120M$. Our results suggest that
for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm
max}$, a universality also apparent in previous perturbative studies in the
regime of small rotation. Using as a stability criterion the absence of
significant relative variations in the horizon areal radius and BH spin, we
find no evidence for any developing instability.
