Statistical mechanics on axially symmetric space-times with the Killing horizon and entropy of rotating black holes in induced gravity - art. no. 024007

We develop a method for computing the free energy of a canonical ensemble o f quantum fields near the horizon of a rotating black hole. We show that th e density of energy levels of a quantum field on a stationary background ca n be related to the density of levels of the same field on a fiducial stati c space-time. The effect of the rotation appears in the additional interact ion of the ''static'' field with a fiducial Abelian gauge potential. The fi ducial 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 sy mmetric 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 concl usions. First, we prove that divergences of the entropy of scaler and spino r fields at the horizon in the presence of rotation have the same form as i n the static case and can be removed by renormalization of the bare black h ole entropy. Second, we demonstrate that a statistical-mechanical represent ation of the Bekenstein-Hawking entropy of a black hole in induced gravity is universal and does not depend on the rotation.