  This is an extended version of our previous letter hep-th/0602146. In this
paper we consider rotating black holes and show that the flux of Hawking
radiation can be determined by anomaly cancellation conditions and regularity
requirement at the horizon. By using a dimensional reduction technique, each
partial wave of quantum fields in a d=4 rotating black hole background can be
interpreted as a (1+1)-dimensional charged field with a charge proportional to
the azimuthal angular momentum m. From this and the analysis gr-qc/0502074,
hep-th/0602146 on Hawking radiation from charged black holes, we show that the
total flux of Hawking radiation from rotating black holes can be universally
determined in terms of the values of anomalies at the horizon by demanding
gauge invariance and general coordinate covariance at the quantum level. We
also clarify our choice of boundary conditions and show that our results are
consistent with the effective action approach where regularity at the future
horizon and vanishing of ingoing modes at r=\infty are imposed (i.e. Unruh
vacuum).
