Hawking radiation for a Proca field in D dimensions II: charged field in a brane charged black hole

TL;DR

This paper extends the analysis of Hawking radiation for a charged Proca field in higher-dimensional black holes, revealing superradiance and charge effects on emission spectra, with most energy emitted on the brane.

Contribution

It introduces a detailed numerical study of charged Proca fields in D-dimensional charged black holes, highlighting superradiance and charge splitting effects.

Findings

Discovery of superradiant modes due to charge.

Inverted charge splitting effect at low energies.

Most emitted energy is on the brane, similar to scalar fields.

Abstract

We generalise our first analysis of the wave equation for a massive vector boson in the background of a D-dimensional Schwarzschild black hole, by adding charge both to the field and the black hole, on the 3+1 dimensional Standard Model brane. A detailed numerical study is performed to obtain the transmission factor for the coupled (as well as decoupled) system of equations describing the Proca field modes, varying the angular momentum number, mass, charge and space-time dimensions. A qualitatively new feature arising from the introduction of charge is the appearance of superradiant modes, which we investigate. We then compute the Hawking fluxes, and analyse the effect of the charge. In particular we observe an inverted charge splitting effect for small energies and for two or more extra dimensions. For neutral fields, we compare the emission of massive particles with spins up to one and also compare the Proca bulk-to-brane ratio of energy emission, showing that, as for a scalar field, most of the energy is emitted on the brane.