  We study the properties of chiral anomalies in a wide class of spacetimes
which possess a principal Killing-Yano tensor. This class includes metrics of
charged rotating black holes as a special physically important case. The
spacetimes which admit a principal Killing-Yano tensor possess a number of
remarkable properties. In particular, such spacetimes have two commuting
Killing vectors and a Killing tensor responsible for their hidden symmetries.
We calculate the gravitational and electromagnetic contributions to the axial
anomaly currents in the spacetime of a charged rotating black hole, and
demonstrate that the equation for the chiral anomaly current has special
solutions which respect both explicit and hidden symmetries. Two of these
solutions have the form of currents propagating along two principal null
directions, which are null eigenvectors of the Riemann tensor. These solutions
describe chiral currents for the incoming and outgoing polarization fluxes. It
is demonstrated that these principal chiral currents can be written explicitly
in the form which contains the off-shell metric coefficients and their
derivatives. We discuss conditions where the principle chiral anomaly current
is regular at the horizon and the axes of symmetry. We demonstrate that for
states where the current vanishes at the past horizon and at the past null
infinity, there exist chirality fluxes at both the future horizon and future
infinity. The latter is directly related to the polarization asymmetry of
Hawking radiation for massless spinning particles. We also calculate the
Chern-Simons currents for both gravitational and electromagnetic chiral
anomalies in the black hole spacetime, and discuss the properties of the
chirality fluxes associated with these currents.
