Hawking Radiation Of The Fermionic Field And Anomaly In (2+1)-dimensional Black Holes

Back in the 70s of 20th century, Christiansen and Fulling proposed that it is possible to use an anomaly in conformal symmetry to derive important constraints on the energy-momentum tensors of quantum fields in a black hole background. In 2005 Sean P. Robinson and Frank Wilczek proposed that one can get the Hawking radiation via the gravitaional anomaly method. They showed that the Hawking radiation is just the cancel term of of the gravita-tional anomaly of the covariant conservation law and gauge invariance.In order to verify the universality of the anomaly cancellation method in deriving the Hawking radiation, we extend gravitational anomaly method to in-vestigate the Hawking radiation of the fermionic field in the (2+1)-dimensional stationary black hole. Using the dimensional reduction technique, we find that the nearhorizon physics for the fermionic field in the background of the general (2+1)-dimensional stationary black hole can be approximated by an infinite col-lection of two-component fermionic fields in the (1+1)-dimensional spacetime background coupled with the dilaton field and U(1) gauge field. By restor-ing the gauge invariance and the general coordinate covariance for the reduced two-dimensional theory, the Hawking flux and temperature of a black hole are obtained.