Hawking Radiation of Fermionic Field and Anomaly in 2+1 Dimensional Black Holes

TL;DR

This paper applies the anomaly cancellation method to derive Hawking radiation for fermionic fields in 2+1 dimensional black holes, including BTZ and BHT massive gravity black holes, using dimensional reduction and symmetry restoration techniques.

Contribution

It extends the anomaly cancellation approach to fermionic fields in 2+1D black holes, demonstrating its applicability to different black hole solutions in three dimensions.

Findings

Hawking flux and temperature are derived for 2+1D black holes.

The method successfully applies to BTZ and BHT massive gravity black holes.

Near-horizon physics reduces to a 1+1D fermionic theory with gauge and dilaton fields.

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 1+1 dimensional spacetime background coupled with dilaton field and U(1) gauge field. By restoring the gauge invariance and the general coordinate covariance for the reduced two dimensional theory, Hawking flux and temperature of black hole are obtained. We apply this method to two types of black holes in three dimensional spacetime, which are BTZ black hole in Einstein gravity and a rotating black hole in Bergshoeff-Hohm-Townsend (BHT) massive gravity.