  The gravitational properties of antimatter are still a secret of nature. One
outstanding possibility is that there is a gravitational repulsion between
matter and antimatter (in short we call it antigravity). We argue that in the
case of antigravity the collapse of a black hole doesn't end with singularity
and that deep inside the horizon, the gravitational field may be sufficiently
strong to create (from the vacuum) neutrino-antineutrino pairs of all flavours.
The created antineutrinos (neutrinos) should be violently ejected outside the
horizon of a black hole composed from matter (antimatter). Our rudimentary
calculations suggest that both, the supermassive black hole in the centre of
our Galaxy and in the centre of the Andromeda Galaxy may produce a flux of
antineutrinos measurable with the new generation of one cubic kilometre
neutrino telescopes. In addition, we suggest two signatures of antigravity in
the case of microscopic black holes which may be eventually produced at CERN:
the decay products should exhibit a strong matter-antimatter asymmetry and the
Hawking radiation should not be the main mechanism for decay.
