  First, we stress that for correct description of highly relativistic fermions
in a gravitational field it is necessary to have an equation which in the
limiting transition to the classical (non-quantum) case corresponds to the
exact Mathisson-Papapetrou equations. According to these equations the spin in
general relativity is Fermi-transported, and the parallel transport of spin is
realized only in some approximation. The traditional general-relativistic Dirac
equation (1929) is based on the parallel transported spinors and does not
ensure the correspondent transition. Second, because in the range of very high
velocity (close to the speed of light) of a spinning particle relative to the
Schwarzschild or Kerr sources the Mathisson-Papapetrou equations have the
solutions which reveal that the spin-gravity interaction acts as a strong
antigravity force, we suppose that this fact can be useful for explanation some
astrophysical phenomena. Some association with the OPERA results is possible.
