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

Hawking Fluxes, $W_\infty$ Algebra and Anomalies