Hawking radiation of the fermionic field and anomaly in (2+1)-dimensional black holes

Abstract

The method of anomaly cancellation to derive Hawking radiation initiated by Robinson and Wilczek is applied to (2+1)-dimensional stationary black holes. Using the dimensional reduction technique, we find that the near-horizon physics for the fermionic field in the background of the general (2+1)-dimensional stationary black hole can be approximated by an infinite collection of two-component fermionic fields in the (1+1)-dimensional spacetime background coupled with the dilaton field and U(1) gauge field. By restoring 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. We apply this method to two types of black holes in three-dimensional spacetime, which are the BTZ black hole in Einstein gravity and a rotating black hole in Bergshoeff–Hohm–Townsend massive gravity.