Ward Identities in the Derivation of Hawking Radiation from Anomalies

TL;DR

This paper clarifies and simplifies the anomaly-based derivation of Hawking radiation, showing that Ward identities and boundary conditions alone suffice without Wess-Zumino terms or effective actions.

Contribution

It demonstrates a streamlined approach to deriving Hawking radiation using Ward identities and boundary conditions, avoiding complex auxiliary terms.

Findings

Ward identities and boundary conditions are sufficient for derivation

The method simplifies technical aspects of previous anomaly-based derivations

Correct Hawking flux is obtained without Wess-Zumino terms

Abstract

Robinson and Wilczek suggested a new method of deriving Hawking radiation by the consideration of anomalies. The basic idea of their approach is that the flux of Hawking radiation is determined by anomaly cancellation conditions in the Schwarzschild black hole (BH) background. Iso et al. extended the method to a charged Reissner-Nordstroem BH and a rotating Kerr BH, and they showed that the flux of Hawking radiation can also be determined by anomaly cancellation conditions and regularity conditions of currents at the horizon. Their formulation gives the correct Hawking flux for all the cases at infinity and thus provides a new attractive method of understanding Hawking radiation. We present some arguments clarifying for this derivation. We show that the Ward identities and boundary conditions for covariant currents without referring to the Wess-Zumino terms and the effective action are sufficient to derive Hawking radiation. Our method, which does not use step functions, thus simplifies some of the technical aspects of the original formulation.