  We perform an explicit calculation of the axial current at finite rotation
and temperature in curved space. We find that finite curvature and mass
corrections to the chiral vortical effect satisfy a relation of the chiral gap
effect, that is, a fermion mass-shift by a scalar curvature. We also point out
that a product term of the angular velocity and the scalar curvature shares the
same coefficient as the mixed gravitational chiral anomaly. We discuss possible
applications of the curvature induced chiral vortical effect to rotating
astrophysical compact objects described by the Kerr metric. Instead of direct
calculation we assume that the Chern-Simons current can approximate the
physical axial current. We make a proposal that the chiral vortical current
from rotating compact objects could provide a novel microscopic mechanism
behind the generation of collimated jets.
