  An attempt is made to promote an analogy between quantized vortex in
condensed matter and black hole: both compact objects have fermion zero modes
which induce the finite temperature of these objects. The motion of the
quantized vortex lines in Fermi superfluids and superconductors leads to the
spectral flow of fermion zero mode. This results in finite temperature and
entropy of the moving vortex. The tunneling transition rate between the
fermionic levels under the influence of the vortex motion suggests the
effective temperature of the vortex core $T_{\rm eff}=(2/\pi) p_Fv_L$, where
$v_L$ is the velocity of the vortex with respect to the heat bath reference
frame and $p_F$ the Fermi momentum. This is an analogue of the Unruh
temperature of the accelerating object in the relativistic system. For the
vortex ring with the radius $R$ this leads to the Hawking type temperature
$T_{\rm vortex~ring}=(\hbar v_F / 2\pi R) \ln (R/r_c)$, where $v_F$ is the
Fermi velocity and $r_c$ is the radius of the vortex core. The corresponding
"Hawking" entropy of the vortex ring of radius $R$ and area $A=\pi R^2$ appears
to be ${\cal S}_{\rm vortex ~ring}=(1/6) A p_F^2$. Similar expression but with
different numerical factor is obtained for the instanton action for the quantum
nucleation of the vortex loop from the homogeneous vacuum, and also for the
"Bekenstein" entropy obtained by counting the number of fermionic bound states
which appear when the vortex loop is created. For the superfluid $^3$He-A,
where some components of the order parameter play the part of the gravitational
field, the Fermi momentum $p_F$ corresponds to the Planck scale for this
effective gravity. The effective action for the gravity field is obtained after
integration over the fermion fields in correspondence with the Sakharov
