Stability of event horizons against neutrino flux: The classical picture

It has been claimed that cosmic censorship conjecture can be violated by quantum tunnelling of neutrinos, though it is strongly supported by classical arguments. We consider the classical interaction of an extremal Kerr black hole with a test massless Dirac field, i.e. a "neutrino field". Evaluating the flux integrals imposed by the energy momentum tensor for fermionic fields and the Killing vectors of the space-time, we prove that this interaction can indeed destroy the event horizon of the black hole and convert it to a naked singularity. The classical process leads to a more generic violation of cosmic censorship conjecture compared to quantum tunnelling processes which occur with a low probability. The range of frequencies of the test neutrino field that can be used to destroy the black hole turns out to be the superradiant range for bosonic fields. We comment on back reaction and quantum effects. We argue that the destruction of black holes by neutrino fields cannot be fixed by self-force effects unlike similar attempts involving test bodies and bosonic fields.