  The condition for the appearance of event horizon is considered in such
pair-correlated systems (superfluids and superconductors) where the fermionic
quasiparticles obey the "relativistic" equations. In these systems, the Landau
critical velocity of superflow corresponds to the speed of light. In
conventional systems, such as s-wave superconductors, the superflow remains
stable even above the Landau treshold. We showed that in the "relativistic"
systems however the quantum vacuum becomes unstable and the superflow collapses
after the "speed of light" is reached, so that horizon cannot appear. Thus an
equilibrium dissipationless superfluid flow state and the horizon are
incompatible due to quantum effects. This negative result is consistent with
the quantum Hawking radiation from the horizon, which would lead to the
dissipation of the flow.
