Chiral anomalies in black hole spacetimes

Abstract

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.