Hawking radiation for a Proca field in D-dimensions

TL;DR

This paper investigates the behavior of massive vector bosons around D-dimensional Schwarzschild black holes, revealing how the mass influences mode coupling, transmission, and Hawking radiation, with implications for black hole phenomenology.

Contribution

It introduces a numerical method to analyze coupled wave equations of Proca fields in higher dimensions and computes transmission factors affecting Hawking radiation.

Findings

Mass term couples vector field modes, affecting their transmission.

Longitudinal modes are excited and contribute significantly to Hawking flux.

Larger angular momentum modes become dominant at intermediate energies.

Abstract

We study the wave equation of a massive vector boson in the background of a D-dimensional Schwarzschild black hole. The mass term introduces a coupling between two physical degrees of freedom of the field, and we solve the resulting system of ODEs numerically, without decoupling. We show how to define decoupled transmission factors from an S-matrix and compute them for various modes, masses and space-time dimensions. The mass term lifts the degeneracy between transverse modes, in D=4, and excites the longitudinal modes, in particular the s-wave. Moreover, it increases the contribution of waves with larger angular momentum, which can be dominant at intermediate energies. The transmission factors are then used to obtain the Hawking fluxes in this channel. Our results alert for the importance of modelling the longitudinal modes correctly, instead of treating them as decoupled scalars as in current black hole event generators; thus they can be used to improve such generators for phenomenological studies of TeV gravity scenarios.