  It has been argued that, starting with a slightly sub-extremal Kerr black
hole instead of an extremal one, it is possible to overspin a black hole past
the extremal limit and turn it into a naked singularity by sending test bodies,
if one neglects radiative and self-force effects. In this work we show that (i)
an extremal Kerr black hole can not be overspun as a result of the interaction
with massless integer spin test fields (scalar, electromagnetic, or
gravitational), (ii) overspinning can be achieved if we start with a nearly
extremal black hole instead, and (iii) for the scalar field, the argument
applies to more general black holes, and also allows use of a more general
field configuration. Our analysis also neglects radiative and self-force
effects.
