Gravitational Anomalies, Hawking Radiation, and Spherically Symmetric Black Holes

TL;DR

This paper investigates gravitational anomalies and Hawking radiation in spherically symmetric black holes, showing how flux deviations from perfect blackbody radiation restore covariance and generalize previous results to dynamic and static spacetimes.

Contribution

It extends the analysis of gravitational anomalies and Hawking flux to arbitrary mass functions and general static spherically symmetric spacetimes, including time-dependent horizons.

Findings

Outgoing flux differs from a perfect blackbody spectrum.

Accounting for flux restores general covariance.

Results apply to both dynamic and static spherically symmetric spacetimes.

Abstract

Motivated by the recent work of Robinson and Wilczek, we evaluate the gravitational anomaly of a chiral scalar field in a Vaidya spacetime of arbitrary mass function, and thus the outgoing flux from the time-dependent horizon in that spacetime. We show that this flux differs from that of a perfect blackbody at a fixed temperature. When this flux is taken into account, general covariance in that spacetime is restored. We also generalize their results to the most general static, and spherically symmetric spacetime.