  Physical phenomena caused by particle's moving faster than light in a space
with multifractal time with dimension close to integer
($d_{t}=1+\epsilon(r(t),t), |\epsilon| \ll 1$ - time is almost homogeneous and
almost isotropic) are considered. The presence of gravitational field is taken
into account. According to the results of the developed by the author theory, a
particle with the rest energy $E_{0}$ would achieve the velocity of light if
given the energy of about $E \sim 10^{3}E_{0}$
