Hawking radiation of a vector field and gravitational anomalies

TL;DR

This paper extends the anomaly-based method for calculating Hawking radiation to include vector fields like photons, showing that electromagnetic fields reduce to scalar fields in black hole backgrounds, and confirming the anomaly cancellation approach.

Contribution

It introduces a formalism for deriving Hawking radiation of vector particles using gravitational anomalies, expanding previous scalar-focused methods to electromagnetic fields.

Findings

Electromagnetic fields reduce to massive scalar fields in black hole backgrounds.

Total energy flux for electromagnetic fields is proportional to that of scalar fields, scaled by (d-2).

Supports Hawking radiation as an anomaly cancellation process on horizons.

Abstract

Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times as that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed.