Anomalies, Hawking Radiations and Regularity in Rotating Black Holes

TL;DR

This paper demonstrates that Hawking radiation flux from rotating black holes can be universally derived using anomaly cancellation and regularity conditions at the horizon, employing a dimensional reduction approach.

Contribution

It extends previous work by applying anomaly cancellation methods to rotating black holes, showing a universal determination of Hawking flux via horizon anomalies.

Findings

Hawking flux can be derived from anomaly conditions at the horizon.

Dimensional reduction interprets partial waves as (1+1)-dimensional charged fields.

Results are consistent with the effective action approach and Unruh vacuum conditions.

Abstract

This is an extended version of our previous letter hep-th/0602146. In this paper we consider rotating black holes and show that the flux of Hawking radiation can be determined by anomaly cancellation conditions and regularity requirement at the horizon. By using a dimensional reduction technique, each partial wave of quantum fields in a d=4 rotating black hole background can be interpreted as a (1+1)-dimensional charged field with a charge proportional to the azimuthal angular momentum m. From this and the analysis gr-qc/0502074, hep-th/0602146 on Hawking radiation from charged black holes, we show that the total flux of Hawking radiation from rotating black holes can be universally determined in terms of the values of anomalies at the horizon by demanding gauge invariance and general coordinate covariance at the quantum level. We also clarify our choice of boundary conditions and show that our results are consistent with the effective action approach where regularity at the future horizon and vanishing of ingoing modes at r=\infty are imposed (i.e. Unruh vacuum).