Can test fields destroy the event horizon in the Kerr-Taub-NUT spacetime?

In this work we investigate if the interaction of the Kerr-Taub-NUT spacetime with test scalar and neutrino fields can lead to the destruction of the event horizon. It turns out that both extremal and nearly extremal black holes can be destroyed by scalar and neutrino fields if the initial angular momentum of the spacetime is sufficiently large relative to its mass and NUT charge. This is the first example in which a classical field satisfying the null energy condition can actually destroy an extremal black hole. For scalar fields, the modes that can lead to the destruction of the horizon are restricted to a narrow range due to superradiance. Since superradiance does not occur for neutrino fields, the destruction of the horizon by neutrino fields is generic, and it cannot be fixed by backreaction effects. We also show that the extremal black holes that can be destroyed by scalar fields correspond to naked singularities in the Kerr limit, in accord with the previous results which imply that extremal Kerr black holes cannot be destroyed by scalar test fields.