  We develop a method for computing the free-energy of a canonical ensemble of
quantum fields near the horizon of a rotating black hole. We show that the
density of energy levels of a quantum field on a stationary background can be
related to the density of levels of the same field on a fiducial static
space-time. The effect of the rotation appears in the additional interaction of
the "static" field with a fiducial abelian gauge-potential. The fiducial static
space-time and the gauge potential are universal, i.e., they are determined by
the geometry of the given physical space-time and do not depend on the spin of
the field. The reduction of the stationary axially symmetric problem to the
static one leads to a considerable simplification in the study of statistical
mechanics and we use it to draw a number of conclusions. First, we prove that
divergences of the entropy of scalar and spinor fields at the horizon in the
presence of rotation have the same form as in the static case and can be
removed by renormalization of the bare black hole entropy. Second, we
demonstrate that statistical-mechanical representation of the
Bekenstein-Hawking entropy of a black hole in induced gravity is universal and
does not depend on the rotation.
