  Non-commutative geometries have been proposed as an approach to quantum
gravity and have led to the construction of non-commutative black holes, whose
interior singularities are purportedly eliminated due to quantum effects. Here
we find evidence that these black holes are in fact unstable, with infalling
matter near the Cauchy (inner) horizon being subject to an infinite blueshift
of the type that has been repeatedly demonstrated for the
Reissner-Nordstr\(\ddot{\text{o}}\)m black hole. This instability is present
even when an ultraviolet cutoff (induced by anticipated non-commutative
geometric effects) to a field propagating in that spacetime is included. We
demonstrate this by following an analogous argument made for
Reissner-Nordstr\(\ddot{\text{o}}\)m black holes, and conclude that stability
is dependent on the surface gravities \(\kappa_-\) and \(\kappa_+\) of the
inner and outer horizons respectively. In general if \(\kappa_- > \kappa_+\),
as we show to be the case here, then the stability of the Cauchy horizon
becomes highly questionable, contrary to recent claims.
