Hawking Fluxes, $W_\infty$ Algebra and Anomalies

TL;DR

This paper analyzes Hawking radiation using anomaly techniques, comparing methods based on trace and diffeomorphism anomalies, and explores the role of $W_$ algebra in higher spin currents and radiation moments.

Contribution

It demonstrates the equivalence of anomaly-based methods for Hawking radiation and highlights the significance of $W_$ algebra in understanding higher moments and currents.

Findings

Trace and diffeomorphism anomaly methods are equivalent.

Higher spin currents lack diffeomorphism anomalies.

$W_$ algebra underpins the predictivity of Hawking radiation calculations.

Abstract

We complete the analysis started in [arXiv:0804.0198] of the Hawking radiation calculated by means of anomaly techniques. We concentrate on a static radially symmetric BH, reduced to two dimensions. We compare the two methods used to derive the integrated Hawking radiation, based on the trace and diffeomorphism anomaly, respectively, and show that they can be reduced to the same basic elements. We then concentrate on higher moments of the Hawking radiation and on higher spin currents, and show that, similarly to trace anomalies, also diffeomorphism anomalies are absent from the conservation laws of higher spin currents. We show that the predictivity of the method is due to the $W_\infty$ current algebra underlying the effective model that describes matter around the black hole.