Covariant anomalies, effective action and Hawking radiation from Kerr-Gödel black hole

The existence of the Gödel rotation parameter in Gödel universe creates many interesting special features for Gödel-type black holes. In this Letter, motivated by the fact that these new features provide additional tests as to the robustness of the covariant anomaly cancellation method and the effective action technique, we attempt to adopt the analyses to study Hawking radiation from Kerr-Gödel black hole. The result is interesting and showing that the covariant anomaly cancellation method and the effective action technique applied to Kerr-Gödel black hole yield Hawking temperatures consistent with the previous results made via other methods.