Anomalies, Hawking Radiation In Taub-NUT Black Hole

Hawking radiation is the most prominent quantum effect in a background space-time with an event horizon. There are several derivations in Hawking Radiation. One from the Hawking's original idea is to compute the Bogoliubov coefficients between in and out states in a black hole background. A tunneling picture is based on pair creations of particles and antiparticles near the horizon and particles will form Hawking radiation ultimately.Recently, another approach to the Hawking effect has been given. It was depicted, instead of four dimensional space-time filed that remains an indeterminable function, that effective field theory become two dimensional and chiral near the event horizon of a black hole by the process of dimensional reduction, and the key technique concludes the Hawking temperature by anomalies theory. On the other hand, Iso, Umetsu and Wilczek further to develop a new method to calculate the total flux of energy-momentum tensor and gauge flux, which fuels the development of Black hole and the determination of physical quantities of Hawking radiation.In this paper, we mainly investigate the anomalous effective action of the Taub-NUT black hole and show that the flux of Hawking Radiation and Temperature can be determined by anomaly cancellation conditions and regularity requirement at the horizon. With the method of a dimensional reduction technique, that is, the (1+1) dimensional quantum anomalies equation, we successfully obtain the simplified metric near the horizon. In addition, the covariant energy-momentum tensor that is related with Hawking temperature are calculated in this black hole.